EP3020043B1 - Optimized scale factor for frequency band extension in an audiofrequency signal decoder - Google Patents

Description

The present invention relates to the field of coding / decoding and audio-frequency signal processing (such as speech, music or other signals) for their transmission or storage.

More particularly, the invention relates to a method and an apparatus for determining an optimized scale factor for adjusting the level of an excitation signal or, in a similar manner, a filter during a band extension. frequency in a decoder or a processor performing audio-frequency signal enhancement.

Many techniques exist to compress (with loss) an audiofrequency signal such as speech or music.

Conventional methods of coding for conversational applications are generally classified in waveform coding (MIC for "Pulse and Coding Modulation", ADPCM for "Pulse Modulation and Adaptive Differential Coding", transform coding ...). , parametric coding (LPC for "Linear Predictive Coding" in English, sinusoidal coding ...) and parametric hybrid coding with a quantification of the parameters by "analysis by synthesis" whose coding CELP (for "Code Excited Linear Prediction" in English) is the best known example.

For non-conversational applications, state of the art audio signal coding (mono) consists of perceptual encoding by transform or subband, with parametric coding of high frequencies by tape replication.
A review of conventional speech and audio coding methods can be found in the books WB Kleijn and KK Paliwal (Eds.), Speech Coding and Synthesis, Elsevier, 1995 ; M. Bosi, RE Goldberg, Introduction to Digital Audio Coding and Standards, Springer 2002 ; J. Benesty, MM Sondhi, Y. Huang (Eds.), Handbook of Speech Processing, Springer 2008 .

Of particular interest here is the 3GPP AMR-WB ("Adaptive Multi-Rate Wideband") codec (decoder and decoder), which operates at an input / output frequency of 16 kHz and in which the signal is divided into two sub-bands, the low band (0-6.4 kHz) which is sampled at 12.8 kHz and coded by CELP model and the high band (6.4-7 kHz) which is parametrically reconstructed by " band extension " ( or BWE for "Bandwidth Extension" with or without additional information depending on the mode of the current frame. It can be noted here that the limitation of the coded band of the AMR-WB codec at 7 kHz is essentially related to the fact that the transmit frequency response of the broadband terminals has been approximated at the time of standardization (ETSI / 3GPP then ITU-T T) according to the frequency mask defined in the ITU-T P.341 standard and more precisely by using a so-called "P341" filter defined in the ITU-T G.191 standard. which cuts frequencies above 7 kHz (this filter respects the mask defined in P.341). However, in theory, it is well known that a signal sampled at 16 kHz may have a defined audio band of 0 to 8000 Hz; the AMR-WB codec thus introduces a limitation of the high band in comparison with the theoretical bandwidth of 8 kHz.

The 3GPP AMR-WB speech codec was standardized in 2001 mainly for circuit-mode (CS) telephony applications over GSM (2G) and UMTS (3G). This same codec was also standardized in 2003 in the ITU-T as Recommendation G.722.2 "Wideband coding speech at around 16kbit / s using Adaptive Multi-Rate Wideband (AMR-WB)".

It includes nine speeds, called modes, from 6.6 to 23.85 kbit / s, and includes continuous transmission mechanisms (DTX for "Discontinuous Transmission") with voice activity detection (VAD for "Voice Activity Detection") and noise generation of comfort (CNG for "Comfort Noise Generation") from frames of silence description (SID for "Silence Insertion Descriptor"), as well as mechanisms of correction of lost frames (FEC for "Frame Erasure Concealment", sometimes called PLC for "Packet Loss Concealment").

The details of the AMR-WB coding and decoding algorithm are not repeated here, a detailed description of this codec can be found in the 3GPP specifications (TS 26.190, 26.191, 26.192, 26.193, 26.194, 26.204) and ITU-TG .722.2 (and the corresponding Annexes and Appendix) and in the article of B. Bessette et al. entitled "The adaptive multirate wideband speech codec (AMR-WB)", IEEE Transactions on Speech and Audio Processing, Vol. 10, no. 8, 2002, pp. 620-636 and the source codes of the associated 3GPP and ITU-T standards.

The principle of band extension in the AMR-WB codec is rather rudimentary. Indeed, the high band (6.4-7 kHz) is generated by formatting a white noise through a temporal envelope (applied in the form of gains per subframe) and frequency (by the application of a linear prediction synthesis filter or LPC for "Linear Predictive Coding"). This band extension technique is illustrated in figure 1 .

• Un premier facteur est calculé (bloc 101) pour mettre le bruit blanc u _HB1(n) (bloc 102) à un niveau semblable à celui de l'excitation, u(n), n = 0..., 63, décodée à 12.8 kHz dans la bande basse : $$u_{\mathit{HB}2}\left(n\right)=u_{\mathit{HB}1}\left(n\right)\sqrt{\frac{{\displaystyle \sum _{l=0}^{63}}u{\left(\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">l</figure-callout>}\right)}^2}{{\displaystyle \sum _{l=0}^{79}{u}_{\mathrm{HB}1}{\left(\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">l</figure-callout>}\right)}^2}}}$$
  

A white noise, u _{H B 1} (n), n = 0, ..., 79, is generated at 16 kHz per subframe of 5 ms per linear congruent generator (block 100). This noise u _{HB 1} ( n) is shaped in time by applying gains per subframe; this operation is broken down into two processing steps (blocks 102, 106 or 109):

• A first factor is calculated (block 101) to set the white noise u _{HB 1} ( n ) (block 102) to a level similar to that of the excitation, u ( n ), n = 0 ..., 63, decoded at 12.8 kHz in the low band: $${\mathrm{<figure-callout\; id="2"\; label="u\; HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}\left(\mathrm{not}\right)={\mathrm{<figure-callout\; id="1"\; label="u\; HB"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}\left(\mathrm{not}\right)\sqrt{\frac{{\displaystyle \underset{l=0}{\overset{63}{\Sigma }}}u{\left(\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">l</figure-callout>}\right)}^2}{{\displaystyle \underset{l=0}{\overset{79}{\Sigma }}{u}_{\mathrm{HB}1}{\left(\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">l</figure-callout>}\right)}^2}}}$$
  

• L'excitation dans la bande haute est ensuite obtenue (bloc 106 ou 109) sous la forme : $$u_{\mathit{HB}}\left(n\right)={\hat{g}}_{\mathit{HB}}{u}_{\mathit{HB}2}\left(n\right)$$
  
  où le gain ĝ_HB est obtenu différemment selon le débit. Si le débit de la trame actuelle est <23.85 kbit/s, le gain ĝ_HB est estimé « en aveugle » (c'est-à-dire sans information supplémentaire); dans ce cas, le bloc 103 filtre le signal décodé en bande basse par un filtre passe-haut ayant une fréquence de coupure à 400 Hz pour obtenir un signal ŝ_hp (n), n = 0,..., 63 - ce filtre passe-haut élimine l'influence des très basses fréquences qui peuvent biaiser l'estimation faite dans le bloc 104 - puis on calcule le « tilt » (indicateur de pente spectrale) noté e_tilt du signal ŝ_hp(n) par autocorrélation normalisée (bloc 104): $$e_{\mathit{tilt}}=\frac{{\displaystyle \sum _{n=1}^{63}}{\hat{s}}_{\mathit{hp}}\left(n\right){\hat{s}}_{\mathit{hp}}\left(n-1\right)}{{\displaystyle \sum _{n=0}^{63}{\hat{s}}_{\mathit{<figure-callout\; id="2"\; label="hp\; n"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">hp</figure-callout>}}{\left(n\right)}^{}{\left(\right)}^2}}$$
  
  et enfin on calcule ĝ_HB sous la forme : $${\hat{g}}_{\mathit{HB}}=w_{\mathit{SP}}{g}_{\mathit{SP}}+\left(1-w_{\mathit{SP}}\right)g_{\mathit{BG}}$$
  
  où g_SP = 1 - e_tilt est le gain appliqué dans les trames actives de parole (SP pour speech), g_BG = 1.25g_SP est le gain appliqué dans les trames inactives de parole associées à un bruit de fond (BG pour Background) et w_SP est une fonction de pondération qui dépend de la détection d'activité vocale (VAD). On comprend que l'estimation du tilt (e_tilt ) permet d'adapter le niveau de la bande haute en fonction de la nature spectrale du signal ; cette estimation est particulièrement importante quand la pente spectrale du signal décodé CELP est telle que l'énergie moyenne décroît quand la fréquence augmente (cas d'un signal voisé où e_tilt est proche de 1, donc g_SP = 1 - e_tilt est ainsi réduit). A noter aussi que le facteur ĝ_HB dans le décodage AMR-WB est borné pour prendre des valeurs dans l'intervalle [0.1, 1.0]. En effet, pour les signaux dont énergie croît quand la fréquence augmente (e_tilt proche de -1, g_SP proche de 2), le gain ĝ_HB est d'habitude sous-estimé.

It can be noted here that the normalization of the energies is done by comparing blocks of different size (64 for u ( n ) and 80 for u _{HB 1} ( n )), without compensation of the differences of sampling frequencies (12.8 or 16 kHz ).

• The excitation in the high band is then obtained (block 106 or 109) in the form: $$u_{\mathit{HB}}\left(\mathrm{not}\right)={\widehat{\mathrm{boy\; Wut}}}_{\mathit{HB}}{u}_{\mathit{<figure-callout\; id="2"\; label="HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">HB</figure-callout>}2}\left(\mathrm{not}\right)$$
  
  where the gain ĝ _HB is obtained differently depending on the flow rate. If the rate of the current frame is <23.85 kbit / s, the gain ĝ _HB is estimated to be "blind" (ie without additional information); in this case, the block 103 filters the decoded low-band signal by a high-pass filter having a cut-off frequency at 400 Hz to obtain a signal ŝ _hp ( n ), n = 0, ..., 63 - this filter high pass eliminates the influence of the very low frequencies which can bias the estimate made in the block 104 - then one calculates the "tilt" (indicator of spectral slope) noted e _tilt of the signal ŝ _hp (n) by autocorrelation normalized ( block 104): $$e_{\mathit{tilt}}=\frac{{\displaystyle \underset{\mathrm{not}=1}{\overset{63}{\Sigma }}}{\hat{s}}_{\mathit{hp}}\left(\mathrm{not}\right){\hat{s}}_{\mathit{hp}}\left(\mathrm{not}-1\right)}{{\displaystyle \underset{\mathrm{not}=0}{\overset{63}{\Sigma }}{\hat{s}}_{\mathit{hp}}{\left(\mathrm{not}\right)}^2}}$$
  
  and finally we calculate ĝ _HB in the form: $${\widehat{\mathrm{boy\; Wut}}}_{\mathit{HB}}=w_{\mathit{SP}}{\mathrm{boy\; Wut}}_{\mathit{SP}}+\left(1-w_{\mathit{SP}}\right){\mathrm{boy\; Wut}}_{\mathit{BG}}$$
  
  where g _SP = 1 - e _tilt is the gain applied in active speech frames (SP for speech), g _BG = 1.25 g _SP is the gain applied in inactive speech frames associated with background noise (BG for Background ) and w _SP is a weighting function that depends on Voice Activity Detection (VAD). It is understood that the estimate of the tilt ( e _tilt ) makes it possible to adapt the level of the high band according to the spectral nature of the signal; this estimate is particularly important when the spectral slope of the decoded signal CELP is such that the average energy decreases when the frequency increases (case of a voiced signal where e _tilt is close to 1, so g _SP = 1 - e _tilt is thus reduced). Note also that the factor ĝ _HB in the AMR-WB decoding is bounded to take values in the interval [0.1, 1.0]. Indeed, for signals whose energy increases when the frequency increases ( e _tilt close to -1, g _SP close to 2), the gain ĝ _HB is usually underestimated.

• A 6.6 kbit/s, le filtre 1/A_HB (z) est obtenu en pondérant par un facteur γ=0.9 un filtre LPC d'ordre 20, 1/Â^ext (z) qui « extrapole » le filtre LPC d'ordre 16, 1/Â(z), décodé dans la bande basse (à 12.8 kHz) - les détails de l'extrapolation dans le domaine des paramètres ISF (pour "Imittance Spectral Frequency" en anglais) sont décrits dans la norme G.722.2 à la section 6.3.2.1; dans ce cas, $$1/A_{\mathit{HB}}\left(z\right)=1/{\hat{A}}^{\mathit{ext}}\left(z/\gamma \right)$$
  
• Aux débits > 6.6 kbit/s, le filtre 1/A_HB (z) est d'ordre 16 et correspond simplement à : $$1/A_{\mathit{HB}}\left(z\right)=1/\hat{A}\left(z/\gamma \right)$$
  
  où γ=0.6. A noter que dans ce cas le filtre 1/Â(zlγ) est utilisé à 16 kHz, ce qui résulte en un étalement (par homothétie) de la réponse en fréquence de ce filtre de [0, 6.4 kHz] à [0, 8 kHz].

Le résultat, s_HB (n), est enfin traité par un filtre passe-bande (bloc 112) de type FIR ("Finite Impulse Response"), pour ne garder que la bande 6 - 7 kHz ; à 23.85 kbit/s, un filtre passe-bas également de type FIR (bloc 113) se rajoute au traitement pour atténuer encore plus les fréquences supérieures à 7 kHz. La synthèse en hautes fréquences (HF) est finalement additionnée (bloc 130) à la synthèse en basses fréquences (BF) obtenue avec les blocs 120 à 122 et ré-échantillonnée à 16 kHz (bloc 123). Ainsi même si la bande haute s'étend en théorie de 6.4 à 7 kHz dans le codec AMR-WB, la synthèse HF est plutôt comprise dans la bande 6-7 kHz avant addition avec la synthèse BF.At 23.85 kbit / s, correction information is transmitted by the encoder AMR-WB and decoded (blocks 107, 108) in order to refine the estimated gain per subframe (4 bits every 5ms, ie 0.8 kbit / s) . The artificial excitation u _HB ( n ) is then filtered (block 111) by a transfer function function LPC (block 111) synthesis filter 1 / A _HB ( z ) and operating at the sampling frequency of 16 kHz. The realization of this filter depends on the rate of the current frame:

• At 6.6 kbit / s, the filter 1 / A _HB ( z ) is obtained by weighting by a factor γ = 0.9 an LPC filter of order 20, 1 / Â ^ext ( z ) which "extrapolates" the order LPC filter. 16, 1 / Â (z), decoded in the low band (at 12.8 kHz) - the details of the extrapolation in the domain of the ISF parameters (for "Imittance Spectral Frequency") are described in the G.722.2 standard in section 6.3.2.1; in that case, $$1/{\mathrm{AT}}_{\mathit{HB}}\left(z\right)=1/{\widehat{\mathrm{AT}}}^{\mathit{ext}}\left(z/\gamma \right)$$
  
• At rates> 6.6 kbit / s, the filter 1 / A _HB ( z ) is of order 16 and simply corresponds to: $$1/{\mathrm{AT}}_{\mathit{HB}}\left(z\right)=1/\widehat{\mathrm{AT}}\left(z/\gamma \right)$$
  
  where γ = 0.6. Note that in this case the filter 1 / Â ( zlγ ) is used at 16 kHz, which results in a spread (by homothety) of the frequency response of this filter from [0, 6.4 kHz] to [0.8] kHz].

The result, s _HB ( n ), is finally processed by a FIR ("Finite Impulse Response") band-pass filter (block 112), to keep only the band 6 - 7 kHz; at 23.85 kbit / s, a low-pass filter of FIR type (block 113) is added to the processing to further attenuate the frequencies above 7 kHz. The high frequency synthesis (HF) is finally added (block 130) to the low frequency synthesis (BF) obtained with the blocks 120 to 122 and resampled at 16 kHz (block 123). Thus, even if the high band theoretically extends from 6.4 to 7 kHz in the AMR-WB codec, the HF synthesis is rather in the band 6-7 kHz before addition with the synthesis BF.

• L'estimation de gains par sous-trame (bloc 101, 103 à 105) n'est pas optimale. Pour partie, elle se base sur une égalisation de l'énergie « absolue » par sous-trame (bloc 101) entre des signaux à des fréquences différentes : l'excitation artificielle à 16 kHz (bruit blanc) et un signal à 12.8 kHz (excitation ACELP décodée). On peut noter en particulier que cette approche induit implicitement une atténuation de l'excitation bande haute (par un ratio 12.8/16=0.8) ; en fait, on notera également qu'aucune désaccentuation (ou déemphase) n'est effectuée sur la bande haute dans le codec AMR-WB, ce qui induit implicitement une amplification relative proche de 0.6 (qui correspond à la valeur de la réponse en fréquence de 1/(1-0.68z ^-1) à 6400 Hz). En fait, les facteurs de 1/0.8 et de 0.6 se compensent approximativement.

• Sur la parole, les tests de caractérisation du codec 3GPP AMR-WB documentés dans le rapport 3GPP TR 26.976 ont montré que le mode à 23.85 kbit/s a une qualité moins bonne qu'à 23.05 kbit/s, sa qualité est en fait similaire à celle du mode à 15.85 kbit/s. Ceci montre en particulier que le niveau du signal HF artificiel doit être contrôlé de façon très prudente, car la qualité est dégradée à 23.85 kbit/s alors que les 4 bits par trame sont sensés permettre de mieux approcher l'énergie des hautes fréquences originales.
• Le filtre passe-bas à 7 kHz (bloc 113) introduit un décalage de près de 1 ms entre les bandes basses et hautes, ce qui peut potentiellement dégrader la qualité de certains signaux en désynchronisant légèrement les deux bandes à 23.85 kbit/s - cette désynchronisation peut également poser problème lors d'une commutation de débit de 23.85 kbit/s à d'autres modes.

Un exemple d'extension de bande par approche temporelle est décrit dans la norme 3GPP TS 26.290 décrivant le codec AMR-WB+ (normalisé en 2005). Cet exemple est illustré dans les schémas-blocs des figures 2a (schéma global) et 2b (prédiction de gain par correction de niveau de réponses) qui correspondent respectivement aux figures 16 et 10 de la spécification 3GPP TS 26.290.
Dans le codec AMR-WB+, le signal d'entrée (mono) échantillonné à la fréquence Fs (en Hz) est divisés en deux bandes de fréquences disjointes, dans lesquelles deux filtres LPC sont calculés et codés séparément:

• un filtre LPC, noté A(z), dans la bande basse (0-Fs/4) - sa version quantifiée est notée Â(z)
• un autre filtre LPC, noté A_HF (z), dans la bande haute repliée spectralement (Fs/4-Fs/2) - sa version quantifiée est notée Â_HF (z)

L'extension de bande se fait dans le codec AMR-WB+ comme détaillé dans les sections 5.4 (codage HF) et 6.2 (décodage HF) de la spécification 3GPP TS 26.290. On en résume ici le principe : l'extension consiste à utiliser l'excitation décodée en basses fréquences (LF excit.) et à mettre en forme cette excitation par un gain temporel par sous-trame (bloc 205) et un filtrage LPC de synthèse (bloc 207) ; de plus, des traitements d'améliorations (post-traitement de l'excitation (bloc 206) et lissage de l'énergie du signal HF reconstruit (bloc 208) sont mis en oeuvre comme illustré à la figure 2a.
Il est important de remarquer que cette extension dans AMR-WB+ nécessite la transmission d'informations supplémentaires : les coefficients du filtre Â_HF (z) en 204 et un gain de mise en forme temporelle par sous-trame (bloc 201). Une particularité de l'algorithme d'extension de bande dans AMR-WB+ est que le gain par sous-trame est quantifié par une approche prédictive ; autrement dit, on ne code pas les gains directement, mais plutôt des corrections de gain qui sont relatives à une estimation du gain notée g_match . Cette estimation, g_match, correspondant en fait à un facteur d'égalisation du niveau entre les filtres Â(z) et Â_HF (z) à la fréquence de séparation entre bande basse et bande haute (Fs/4). Le calcul du facteur g_match (bloc 203) est détaillé à la figure 10 de la spécification 3GPP TS 26.290 reprise ici à la figure 2b. On ne détaillera pas plus ici cette figure. On retiendra pour résumer que les blocs 210 à 213 servent à calculer l'énergie de la réponse impulsionnelle de $\frac{\hat{A}\left(\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">z</figure-callout>}\right)}{\left(1-0.9z^{-1}\right){\hat{A}}_{\mathit{HF}}\left(z\right)},$

en se rappelant que le filtre Â_HF (z) modélise une bande haute repliée spectrale (à cause des propriétés spectrales du banc de filtre séparant les bandes basse et haute). Puisque les filtres sont interpolés par sous-trames, le gain g_match n'est calculé qu'une fois par trame, et il est interpolé par sous-trames.
La technique de codage des gains d'extension de bande dans AMR-WB+, et plus précisément la compensation de niveaux des filtres LPC en leur point de jonction, est une méthode adaptée dans le contexte d'une extension de bande par modèles LPC en bande basse et haute, et on peut remarquer qu'une telle compensation de niveau entre filtres LPC n'est pas présente dans l'extension de bande du codec AMR-WB. Cependant, on peut vérifier dans la pratique que l'égalisation directe du niveau entre les deux filtres LPC à la fréquence de séparation n'est pas une méthode optimale et peut provoquer une surestimation d'énergie en bande-haute et des artefacts audibles dans certains cas ; on rappelle qu'un filtre LPC représente une enveloppe spectrale, ainsi le principe de l'égalisation du niveau entre deux filtres LPC pour une fréquence donnée revient à ajuster le niveau relatif de deux enveloppes LPC. Or un telle égalisation réalisée en une fréquence précise n'assure pas une complète continuité et cohérence globale de l'énergie (en fréquence) au voisinage du point d'égalisation lorsque l'enveloppe fréquentielle du signal fluctue de façon significative dans ce voisinage. Une façon mathématique de poser le problème consiste à remarquer que la continuité entre deux courbes peut être assurée en les forçant à se rejoindre en un même point, mais rien ne garantit que les propriétés locales (dérivées successives) coïncident de façon à assurer une cohérence plus globale. Le risque en assurant une continuité ponctuelle entre des enveloppes LPC bandes basse et haute est de fixer l'enveloppe de LPC en bande haute à un niveau relatif trop fort ou trop faible, le cas d'un niveau trop fort étant plus dommageable car il résulte en des artefacts plus gênants.
Par ailleurs, la compensation de gain dans AMR-WB+ est avant tout une prédiction du gain connue au codeur et au décodeur et qui sert à réduire le débit nécessaire à la transmission d'information de gain mettant à l'échelle le signal d'excitation bande haute. Or, dans le contexte d'une amélioration du codage/décodage AMR-WB de façon interopérable, il n'est pas possible de modifier le codage existant des gains par sous-trames (0.8 kbit/s) de l'extension de bande dans le mode 23.85 kbit/s d'AMR-WB. De plus, pour les débits strictement inférieurs à 23.85 kbit/s, la compensation de niveaux de filtres LPC en bandes basse et haute peut être appliquée dans l'extension de bande d'un décodage compatible avec AMR-WB, cependant l'expérience montre que cette seule technique dérivée du codage AMR-WB+, appliquée sans optimisation, peut engendrer des problèmes de surestimation d'énergie de la bande haute (>6 kHz).
Il existe donc un besoin pour améliorer la compensation de gains entre des filtres de prédiction linéaire de bande de fréquences différentes pour l'extension de bande de fréquence dans un codec de type AMR-WB ou une version interopérable de ce codec sans pour autant surestimer l'énergie dans une bande de fréquence et sans nécessiter d'informations supplémentaires du codeur.Several disadvantages can be identified with the AMR-WB codec band extension technique, in particular:

• The estimation of gains per subframe (block 101, 103 to 105) is not optimal. In part, it is based on an equalization of the "absolute" energy per sub-frame (block 101) between signals at different frequencies: the artificial excitation at 16 kHz (white noise) and a signal at 12.8 kHz ( ACELP excitation decoded). It may be noted in particular that this approach implicitly induces an attenuation of the excitation band high (by a ratio 12.8 / 16 = 0.8); in fact, it will also be noted that no deemphasis (or deemphasis) is performed on the high band in the AMR-WB codec, which implicitly induces a relative amplification close to 0.6 (which corresponds to the value of the frequency response from 1 / (1-0.68 z ^-1 ) to 6400 Hz). In fact, the factors of 1 / 0.8 and 0.6 compensate each other approximately.

• On the talk, the 3GPP AMR-WB codec characterization tests documented in the 3GPP TR 26.976 report showed that the 23.85 kbit / sa mode is not as good as 23.05 kbit / s, its quality is actually similar to that of the 15.85 kbit / s mode. This shows in particular that the level of artificial RF signal must be controlled very carefully, because the quality is degraded to 23.85 kbit / s while the 4 bits per frame are supposed to better approach the energy of the original high frequencies.
• The 7 kHz low-pass filter (block 113) introduces an offset of almost 1 ms between the low and high bands, which can potentially degrade the quality of some signals by slightly desynchronizing the two bands at 23.85 kbit / s - this Desynchronization can also be a problem when switching from 23.85 kbit / s to other modes.

An example of a time approach band extension is described in the 3GPP TS 26.290 standard describing the AMR-WB + codec (standardized in 2005). This example is illustrated in the block diagrams of Figures 2a (global scheme) and 2b (response level correction gain prediction) which respectively correspond to Figures 16 and 10 of 3GPP specification TS 26.290.
In the AMR-WB + codec, the input signal (mono) sampled at the frequency Fs (in Hz) is divided into two disjointed frequency bands, in which two LPC filters are calculated and separately coded:

• an LPC filter, denoted A (z), in the low band (0, Fs / 4) - its quantized version is denoted  (z)
• another LPC filter, denoted A _HF (z), in the upper spectrally folded strip (Fs / 4-Fs / 2) - its quantized version is denoted  _HF (z)

The band extension is done in the AMR-WB + codec as detailed in sections 5.4 (HF coding) and 6.2 (HF decoding) of the 3GPP specification TS 26.290. Here we summarize the principle: the extension consists in using the decoded excitation at low frequencies (LF excit.) And in shaping this excitation by a temporal gain per subframe (block 205) and a synthesis LPC filtering (block 207); in addition, enhancement treatments (post-treatment excitation (block 206) and smoothing the energy of the reconstructed RF signal (block 208) are implemented as illustrated in FIG. figure 2a .
It is important to note that this extension in AMR-WB + requires the transmission of additional information: the coefficients of the filter  _HF (z) 204 and a temporal shaping gain per subframe (block 201). A peculiarity of the band extension algorithm in AMR-WB + is that subframe gain is quantified by a predictive approach; in other words, we do not code gains directly, but rather gain corrections that relate to an estimate of the gain noted g _match . This estimate, g _match , actually corresponds to a level equalization factor between the λ (z) and λ _HF (z) filters at the separation frequency between low band and high band (Fs / 4). The calculation of the g _match factor (block 203) is detailed in Figure 10 of the 3GPP specification TS 26.290, reproduced here at figure 2b . We will not detail here this figure. To summarize, blocks 210 to 213 are used to calculate the energy of the impulse response of $\frac{\widehat{\mathrm{AT}}\left(z\right)}{\left(1-0.9z^{-1}\right){\widehat{\mathrm{AT}}}_{\mathit{HF}}\left(z\right)},$

remembering that the _HF filter (z) models a spectral folded high band (because of the spectral properties of the filter bank separating the low and high bands). Since the filters are interpolated by subframes, the gain g _match is calculated only once per frame, and it is interpolated by subframes.
The technique of coding bandwidth gains in AMR-WB +, and more specifically the level compensation of LPC filters at their junction point, is a suitable method in the context of band-based LPC bandwidth expansion. low and high, and it can be noticed that such level compensation between LPC filters is not present in the band extension of the AMR-WB codec. However, it can be verified in practice that the direct equalization of the level between the two LPC filters at the separation frequency is not an optimal method and can cause an overestimation of high-band energy and audible artifacts in some case; It is recalled that an LPC filter represents a spectral envelope, so the principle of equalizing the level between two LPC filters for a given frequency amounts to adjusting the relative level of two LPC envelopes. However, such equalization performed at a precise frequency does not ensure complete continuity and overall coherence of the energy (in frequency) in the vicinity of the equalization point when the frequency envelope of the signal fluctuates significantly in this vicinity. A mathematical way of posing the problem consists in noting that the continuity between two curves can be assured by forcing them to meet at the same point, but there is no guarantee that the local properties (successive derivatives) coincide in order to ensure a more coherent overall. The risk in ensuring point-to-point continuity between low and high band LPC envelopes is to set the LPC envelope in band high at a relative level too strong or too weak, the case of a too strong level being more damaging because it results in more troublesome artifacts.
Furthermore, the gain compensation in AMR-WB + is primarily a prediction of the known gain to the encoder and the decoder and which serves to reduce the bit rate necessary for the transmission of gain information scaling the excitation signal. high band. However, in the context of improved interoperable AMR-WB coding / decoding, it is not possible to modify the existing coding of subframe gains (0.8 kbit / s) of the band the 23.85 kbit / s mode of AMR-WB. In addition, for bit rates strictly below 23.85 kbit / s, high and low band LPC filter level compensation can be applied in the bandwidth of an AMR-WB compatible decoding, however the experiment shows that this technique derived from the AMR-WB + coding, applied without optimization, can cause problems of overestimation of energy of the high band (> 6 kHz).
There is therefore a need to improve the gain compensation between linear frequency band prediction filters of different frequencies for the frequency band extension in an AMR-WB codec or an interoperable version of this codec without overestimating the energy in a frequency band and without requiring additional information from the coder.

The present invention improves the situation.

• détermination d'un filtre de prédiction linéaire dit filtre additionnel, d'ordre inférieur au filtre de prédiction linéaire de la première bande de fréquence, les coefficients du filtre additionnel étant obtenus à partir des paramètres décodés ou extraits de la première bande de fréquence; et
• calcul du facteur d'échelle optimisé en fonction au moins des coefficients du filtre additionnel.

For this purpose, the invention provides a method for determining an optimized scale factor to be applied to an excitation signal or a filter during a frequency band extension process of an audio frequency signal, the band extension method comprising a step of decoding or extracting, in a first frequency band, an excitation signal and parameters of the first frequency band comprising coefficients of a linear prediction filter a step of generating an extended excitation signal on at least a second frequency band and a filtering step by a linear prediction filter for the second frequency band. The determination method is such that it comprises the following steps:

• determining a linear prediction filter called additional filter, of order less than the linear prediction filter of the first frequency band, the coefficients of the additional filter being obtained from the parameters decoded or extracted from the first frequency band; and
• calculating the scaling factor optimized according to at least the coefficients of the additional filter.

Thus, the use of an additional filter of a lower order than the filter of the first frequency band to be equalized makes it possible to avoid overestimations of energy in the high frequencies which could result from local fluctuations of the envelope and which can disrupt the equalization of the prediction filters.

The equalization of gains between the linear prediction filters of the first and second frequency band is thus improved.

In an advantageous application of the optimized scale factor thus obtained, the band extension method comprises a step of applying the optimized scaling factor to the extended excitation signal.

In a suitable embodiment, the application of the optimized scaling factor is combined with the filtering step in the second frequency band.

Thus the steps of filtering and applying the optimized scaling factor are combined with a single filtering step to reduce the processing complexity.

In a particular embodiment, the coefficients of the additional filter are obtained by truncation of the transfer function of the linear prediction filter of the first frequency band to obtain a lower order.

This additional low-order filter is thus obtained in a simple manner.

In addition, in order to obtain a stable filter, the coefficients of the additional filter are modified according to a criterion of stability of the additional filter.

• calcul des réponses en fréquence des filtres de prédiction linéaire des première et deuxième bandes de fréquence pour une fréquence commune;
• calcul de la réponse en fréquence du filtre additionnel pour cette fréquence commune;
• calcul du facteur d'échelle optimisé en fonction des réponses en fréquence ainsi calculées.

In a particular embodiment, the computation of the optimized scaling factor comprises the following steps:

• calculating the frequency responses of the linear prediction filters of the first and second frequency bands for a common frequency;
• calculating the frequency response of the additional filter for this common frequency;
• calculation of the optimized scale factor according to the frequency responses thus calculated.

Thus, the optimized scaling factor is calculated to avoid annoying artifacts that might arise in the event that the higher order filter frequency response of the first band near the common frequency would reveal a peak or a valley. of the signal.

• première mise à l'échelle du signal d'excitation étendu par un gain calculé par sous-trame fonction d'un rapport d'énergie entre le signal d'excitation décodé et le signal d'excitation étendu;
• deuxième mise à l'échelle du signal d'excitation issu de la première mise à l'échelle par un gain de correction décodé;
• ajustement de l'énergie de l'excitation pour la sous-trame courante par un facteur d'ajustement calculé en fonction de l'énergie du signal obtenu après la deuxième mise à l'échelle et en fonction du signal obtenu après application du facteur d'échelle optimisé.

In a particular embodiment, the method further comprises the following steps, implemented for a predetermined decoding rate:

• first scaling of the extended excitation signal by a subframe calculated gain as a function of an energy ratio between the decoded excitation signal and the extended excitation signal;
• second scaling of the excitation signal from the first scaling by a decoded correction gain;
• adjusting the excitation energy for the current subframe by an adjustment factor calculated as a function of the energy of the signal obtained after the second scaling and as a function of the signal obtained after applying the factor d optimized scale.

Thus, additional information can be used to improve the quality of the extended signal for a predetermined mode of operation.

• un module de détermination d'un filtre de prédiction linéaire dit filtre additionnel, d'ordre inférieur au filtre de prédiction linéaire de la première bande de fréquence, les coefficients du filtre additionnel étant obtenus à partir des paramètres décodés ou extraits de la première bande de fréquence; et
• un module de calcul du facteur d'échelle optimisé en fonction au moins des coefficients du filtre additionnel.

The invention also relates to a device for determining an optimized scale factor to be applied to an excitation signal or to a filter in a frequency band extension device of an audiofrequency signal, the extension device band comprising a decoding or extraction module, in a first frequency band, of an excitation signal and parameters of the first frequency band comprising coefficients of a linear prediction filter, a generation module an excitation signal extended over at least a second frequency band and a filtering module by a linear prediction filter for the second frequency band. The determination device is such that it comprises:

• a module for determining a linear prediction filter called additional filter, of a lower order than the linear prediction filter of the first frequency band, the coefficients of the additional filter being obtained from the parameters decoded or extracted from the first band of frequency; and
• a module for calculating the scaling factor optimized according to at least the coefficients of the additional filter.

The invention relates to a decoder comprising a device as described.

It relates to a computer program comprising code instructions for implementing the steps of the method of determining an optimized scale factor as described, when these instructions are executed by a processor.

Finally, the invention relates to a storage medium, readable by a processor, integrated or not to the device for determining an optimized scaling factor, possibly removable, storing a computer program implementing a method of determining a optimized scaling factor as previously described.

• la figure 1 illustre une partie d'un décodeur de type AMR-WB mettant en oeuvre des étapes d'extension de bande de fréquence de l'état de l'art et tel que décrit précédemment;
• les figures 2a et 2b présentent le codage de la bande haute dans le codec AMR-WB+ selon l'état de l'art et tel que décrit précédemment;
• la figure 3 illustre un décodeur interopérable avec le codage AMR-WB et intégrant un dispositif d'extension de bande utilisé selon un mode de réalisation de l'invention ;
• la figure 4 illustre un dispositif de détermination d'un facteur d'échelle optimisé par sous-trame en fonction du débit, selon un mode de réalisation de l'invention; et
• les figures 5a et 5b illustrent les réponses en fréquences des filtres utilisées pour le calcul du facteur d'échelle optimisé selon un mode de réalisation de l'invention;
• la figure 6 illustre sous forme d'organigramme, les étapes principales d'un procédé de détermination d'un facteur d'échelle optimisé selon un mode de réalisation de l'invention;
• la figure 7 illustre un mode de réalisation dans le domaine fréquentiel d'un dispositif de détermination de facteur d'échelle optimisé lors d'une extension de bande;
• la figure 8 illustre une réalisation matérielle d'un dispositif de détermination de facteur d'échelle optimisé lors d'une extension de bande selon l'invention.

Other features and advantages of the invention will appear more clearly on reading the following description, given solely by way of nonlimiting example, and with reference to the appended drawings, in which:

• the figure 1 illustrates a part of an AMR-WB type decoder implementing frequency band extension steps of the state of the art and as described above;
• the Figures 2a and 2b present the coding of the high band in the AMR-WB + codec according to the state of the art and as previously described;
• the figure 3 illustrates an interoperable decoder with the AMR-WB encoding and incorporating a band extension device used according to an embodiment of the invention;
• the figure 4 illustrates a device for determining a subframe-optimized scale factor as a function of the flow rate, according to one embodiment of the invention; and
• the Figures 5a and 5b illustrate the frequency responses of the filters used for calculating the optimized scale factor according to one embodiment of the invention;
• the figure 6 illustrates in flowchart form the main steps of a method for determining an optimized scale factor according to an embodiment of the invention;
• the figure 7 illustrates a frequency domain embodiment of an optimized scale factor determination device during a band extension;
• the figure 8 illustrates a hardware realization of an optimized scale factor determination device during a band extension according to the invention.

The figure 3 illustrates an exemplary decoder, compatible with the AMR-WB / G.722.2 standard, in which there is a band extension comprising a determination of an optimized scale factor according to one embodiment of the method of the invention, implemented implemented by the tape extension device illustrated by block 309.

Unlike AMR-WB decoding which operates with an output sampling frequency of 16 kHz, we consider here a decoder that can operate with an output signal (synthesis) at the frequency fs = 8, 16, 32 or 48 kHz. Note that it is assumed here that the coding was performed according to the AMR-WB algorithm with an internal frequency of 12.8 kHz for the CELP coding in low band and 23.85 kbit / s with a gain coding per subframe to the frequency of 16 kHz; even if the invention is described here at the decoding level, it is assumed here that the coding can also operate with an input signal at the frequency fs = 8, 16, 32 or 48 kHz and adequate resampling operations, beyond the scope of the invention, are implemented in coding as a function of the value of fs. It can be noted that when fs = 8 kHz, in the case of a decoding compatible with AMR-WB, it is not necessary to extend the low band 0-6.4 kHz, because the audio band reconstructed at the frequency fs is limited to 0-4000 Hz.

To the figure 3 , the CELP decoding (BF for low frequencies) still operates at the internal frequency of 12.8 kHz, as in AMR-WB, and the band extension (HF for high frequencies) used for the invention operates at the frequency of 16 kHz , the syntheses BF and HF are combined (block 312) at the frequency fs after adequate resampling (block 306 and internal processing block 311). In alternative embodiments, the combination of the low and high bands may be done at 16 kHz, after resampling the low band of 12.8 to 16 kHz, before resampling the combined signal at the frequency fs .

• Démultiplexage des paramètres codés (bloc 300) en cas de trame correctement reçue (bfi=0 où bfi est le « bad frame indicator » valant 0 pour une trame reçue et 1 pour une trame perdue)
• Décodage des paramètres ISF avec interpolation et conversion en coefficients LPC (bloc 301) comme décrit dans la clause 6.1 de la norme G.722.2.
• Décodage de l'excitation CELP (bloc 302), avec une partie adaptative et fixe pour reconstruire l'excitation (exc ou u'(n)) dans chaque sous-trame de longueur 64 à 12.8 kHz: $$u\prime \left(n\right)={\hat{g}}_{p}v\left(n\right)+{\hat{g}}_{c}c\left(n\right),\mathit{n}=0,\cdots ,63$$
  
  en suivant les notations de la clause 7.1.2.1 de la recommandation ITU-T G.718 d'un décodeur interopérable avec le codeur/décodeur AMR-WB, concernant le décodage CELP, où v(n) et c(n) sont respectivement les mots de code des dictionnaires adaptatif et fixe, et ĝ_p et ĝ_c sont les gains décodés associés. Cette excitation u'(n) est utilisée dans le dictionnaire adaptatif de la sous-trame suivante ; elle est ensuite post-traitée et on distingue comme dans G.718 l'excitation u'(n) (aussi notée exc) de sa version post-traitée modifiée u(n) (aussi notée exc2) qui sert d'entrée au filtre de synthèse, 1/Â(z), dans le bloc 303.
• Filtrage de synthèse par 1/Â(z) (bloc 303) où le filtre LPC décodé Â(z) est d'ordre 16
• Post-traitement bande étroite (bloc 304) selon la clause 7.3 de G.718 si fs=8 kHz.
• Désaccentuation (bloc 305) par le filtre 1/(1 - 0.68z ^-1)
• Post-traitement des basses fréquences (dit « bass posfilter ») (bloc 306) atténuant le bruit inter-harmonique en basses fréquences tel que décrit à la clause 7.14.1.1 de G.718. Ce traitement introduit un retard qui est pris en compte dans le décodage de la bande haute (>6.4 kHz).
• Ré-échantillonnage de la fréquence interne de 12.8 kHz à la fréquence de sortie fs (bloc 307). Plusieurs réalisations sont possibles. Sans perte de généralité, on considère ici à titre d'exemple que si fs=8 ou 16 kHz, le ré-échantillonnage décrit dans la clause 7.6 de G.718 est repris ici, et si fs=32 ou 48 kHz, des filtres à réponse impulsionnelle finie (FIR) supplémentaires sont utilisés.
• Calcul des paramètres du "noise gate" (bloc 308) qui est réalisé de façon préférentielle comme décrit dans la clause 7.14.3 de G.718 pour « améliorer » la qualité des silences par réduction du niveau.

Dans des variantes qui peuvent être mises en oeuvre pour l'invention, les post-traitements appliqués à l'excitation peuvent être modifiés (par exemple, la dispersion de phase peut être améliorée) ou ces post-traitements peuvent être étendus (par exemple, une réduction du bruit inter-harmonique peut être mise en oeuvre), sans affecter la nature de l'extension de bande.
On peut noter que l'utilisation des blocs 306, 308, 314 est optionnelle.
On notera également que le décodage de la bande basse décrit ci-dessus suppose une trame courante dite « active » avec un débit entre 6.6 et 23.85 kbit/s. En fait, quand le mode DTX (transmission continue en français) est activé, certaines trames peuvent être codées comme « inactives » et dans ce cas on peut soit transmettre un descripteur de silence (sur 35 bits) soit ne rien transmettre. En particulier, on rappelle que la trame SID décrit plusieurs paramètres : paramètres ISF moyennés sur 8 trames, énergie moyenne sur 8 trames, flag de "dithering" pour la reconstruction de bruit non stationnaire. Dans tous les cas, au décodeur, on retrouve le même modèle de décodage que pour une trame active, avec une reconstruction de l'excitation et d'un filtre LPC pour la trame courante, ce qui permet d'appliquer l'extension de bande même sur des trames inactives. Le même constat s'applique pour le décodage de « trames perdues » (ou FEC, PLC) dans lequel le modèle LPC est appliqué.Decoding according to the figure 3 depends on the mode (or rate) AMR-WB associated with the current frame received. As an indication and without this having an effect on block 309, the decoding of the low band CELP part comprises the following steps:

• Demultiplexing the coded parameters (block 300) in the case of a correctly received frame ( bfi = 0 where bfi is the " bad frame indicator " equal to 0 for a received frame and 1 for a lost frame)
• Decoding ISF parameters with interpolation and conversion to LPC coefficients (block 301) as described in clause 6.1 of G.722.2.
• CELP excitation decoding (block 302), with an adaptive and fixed part to reconstruct the excitation (exc or u ' ( n )) in each subframe of length 64 to 12.8 kHz: $$u\text{'}\left(\mathrm{not}\right)={\widehat{\mathrm{boy\; Wut}}}_{p}v\left(\mathrm{not}\right)+{\widehat{\mathrm{boy\; Wut}}}_{\mathrm{vs}}\mathrm{vs}\left(\mathrm{not}\right),\mathit{not}=0,\cdots ,63$$
  
  by following the notation of clause 7.1.2.1 of ITU-T Recommendation G.718 of an interoperable decoder with the AMR-WB encoder / decoder, concerning CELP decoding, where v (n) and c ( n ) are respectively the adaptive and fixed dictionaries codewords, and ĝ _p and ĝ _c are the associated decoded gains. This excitation u ' ( n ) is used in the adaptive dictionary of the following subframe; it is then post-processed and one discerns as in G.718 the excitation u ' ( n ) (also noted exc) of its modified post-processed version u ( n ) (also noted exc2) which serves as input to the filter synthesis, 1 / Â (z), in block 303.
• Synthetic filtering by 1 /  (z) (block 303) where the decoded LPC filter  (z) is of order 16
• Aftertreatment narrow band (block 304) according to clause 7.3 of G.718 if fs = 8 kHz.
• Deactivation (block 305) by the filter 1 / (1 - 0.68 z ^-1 )
• Low-frequency post-processing (so-called " bass posfilter ") (block 306) attenuating inter-harmonic noise at low frequencies as described in clause 7.14.1.1 of G.718. This processing introduces a delay which is taken into account in the decoding of the high band (> 6.4 kHz).
• Resampling of the internal frequency from 12.8 kHz to the output frequency fs (block 307). Several achievements are possible. Without loss of generality, we consider here as an example that if fs = 8 or 16 kHz, the resampling described in clause 7.6 of G.718 is repeated here, and if fs = 32 or 48 kHz, filters Finite Impulse Response (FIR) are used.
• Calculation of the "noise gate" parameters (block 308) which is preferably performed as described in clause 7.14.3 of G.718 to "improve" the quality of the silences by reducing the level.

In variants that can be implemented for the invention, the post-treatments applied to the excitation can be modified (for example, the phase dispersion can be improved) or these post-treatments can be extended (for example, a reduction of the inter-harmonic noise can be implemented), without affecting the nature of the band extension.
It can be noted that the use of blocks 306, 308, 314 is optional.
Note also that the decoding of the low band described above assumes a current frame called "active" with a rate between 6.6 and 23.85 kbit / s. In fact, when the DTX (Continuous Transmission in French) mode is activated, some frames can be coded as "inactive" and in this case you can either transmit a silence descriptor (on 35 bits) or not transmit anything. In particular, it is recalled that the SID frame describes several parameters: ISF parameters averaged over 8 frames, average energy over 8 frames, "dithering" flag for the non-stationary noise reconstruction. In all cases, at the decoder, we find the same decoding model as for an active frame, with a reconstruction of the excitation and an LPC filter for the current frame, which makes it possible to apply the band extension. even on inactive frames. The same applies for the decoding of "lost frames" (or FEC, PLC) in which the LPC model is applied.

In the embodiment described here and with reference to the figure 7 ,, the decoder makes it possible to extend the decoded low band (50-6400 Hz taking into account the high-pass filtering at 50 Hz at the decoder, 0-6400 Hz in the general case) with an extended band whose width varies, ranging from approximately 50-6900 Hz to 50-7700 Hz depending on the mode implemented in the current frame. We can talk about a first frequency band from 0 to 6400Hz and a second frequency band from 6400 to 8000Hz. In reality, in the preferred embodiment, the extension of the excitation is carried out in the frequency domain in a band of 5000 to 8000 Hz, to allow bandpass filtering of width 6000 to 6900 or 7700 Hz.

At 23.85 kbit / s, the HF gain correction information (0.8 kbit / s) transmitted at 23.85 kbit / s is decoded here. Its use is detailed below, with reference to the figure 4 . The high band synthesis part is performed in block 309 representing the band extension device used for the invention and which is detailed in FIG. figure 7 in one embodiment.

In order to align the decoded low and high bands, a delay (block 310) is introduced to synchronize the outputs of the blocks 306 and 307 and the high band synthesized at 16 kHz is resampled from 16 kHz to the fs frequency (block output 311). The value of the delay T depends on how to synthesize the high band signal, the frequency fs as well as the post-processing of the low frequencies. Thus, in general, the value of T in the block 310 will have to be adjusted according to the specific implementation.

The low and high bands are then combined (added) in block 312 and the resulting synthesis is post-processed by high-order 50 Hz (type IIR) high-pass filtering whose coefficients depend on the frequency fs (block 313) and output postprocessing with optional "noisegate" application similar to G.718 (block 314).

With reference to the figure 3 an embodiment of an optimized scale factor determining device to be applied to an excitation signal in a frequency band extension process is now described. This device is included in the band extension block 309 previously described.

Thus, the block 400, from a decoded excitation signal in a first frequency band u ( n ), performs a band extension to obtain an extended excitation signal u _HB ( n ) on at least a second frequency band.

It will be noted here that the optimized scale factor estimation according to the invention is independent of how to obtain the signal u _HB ( n ) . A condition regarding its energy is important, however. Indeed, it is necessary that the energy of the high band of 6000 to 8000 Hz is at a level similar to the energy of the band 4000 to 6000 Hz of the decoded excitation signal at the output of the block 302. since the low-band signal is de-emphasized (block 305), it is also necessary to apply the de-emphasis to the high-band excitation signal, either by using an own de-emphasis filter or by multiplying by a constant factor which corresponds to a mean attenuation of mentioned filter. This condition does not apply to the 23.85 kbit / s rate that uses the additional information transmitted by the encoder. In this case, the energy of the high band excitation signal must be consistent with the signal energy corresponding to the encoder, as explained later.

The frequency band extension may for example be implemented in the same way as for the AMR-WB decoder described with reference to FIG. figure 1 in blocks 100 to 102, from a white noise.

In another embodiment, this band extension can be performed from a combination of a white noise and a decoded excitation signal as illustrated and subsequently described for blocks 700 to 707 of FIG. figure 7 .

Other frequency band extension methods with conservation of the energy level between the decoded excitation signal and the extended excitation signal as described below, can of course be envisaged for the block 400.

In addition, the tape expansion module may also be independent of the decoder and may extend a band of an existing audio signal stored or transmitted to the expansion module, with an analysis of the audio signal to extract one excitation and a LPC filter. In this case, the excitation signal at the input of the extension module is no longer a decoded signal but a signal extracted after analysis, as well as the coefficients of the linear prediction filter of the first frequency band used in the method of determining the optimized scale factor in an implementation of the invention.

In the example shown in figure 4 First of all, we consider the case of rates <23.85 kbit / s, for which the determination of the optimized scale factor is limited to block 401. In this case, we calculate an optimized scaling factor, denoted g _HB2 ( m ) . In one embodiment, this calculation is preferably carried out by subframe and it consists in equalizing the levels of the frequency responses of the LPC filters 1 / Â (z) and 1 / Å (z / γ ) used in low and high frequencies. high frequencies, as described later with reference to the figure 7 , with extra care to avoid the cases of overestimations that can result in too much energy from the synthesized high band and thus generate audible artifacts.
In an alternative embodiment, it will be possible to keep the extrapolated HF synthesis filter 1 / Â ^ext (z / γ ) as implemented in the AMR-WB decoder or a decoder interoperable with the AMR-WB encoder / decoder, by example according to ITU-T Recommendation G.718, instead of filter 1 / Â (z / γ ). The compensation according to the invention is then performed from filters 1 / A (z) and 1 / Â ^ext (z / γ ).
The determination of the optimized scale factor is also performed by the determination (in 401a) of a linear prediction filter called additional filter, of a lower order than the linear prediction filter of the first frequency band 1 / Å (z ), the coefficients of the additional filter being obtained from the parameters decoded or extracted from the first frequency band. The optimized scaling factor is then calculated (at 401b) based on at least one of these coefficients to be applied to the extended excitation signal u _HB ( n ).

où M = 16 est l'ordre du filtre LPC décodé 1/Â(z), et θ correspond à la fréquence de 6000 Hz normalisée pour la fréquence d'échantillonnage de 12.8 kHz, soit : $$\theta =2\pi \frac{6000}{12800}\mathrm{.}$$

Ensuite, de façon similaire, on calcule : $$P=\frac{1}{\left|\hat{A}\left(e^{\mathit{j\theta }\prime }/\gamma \right)\right|}=\frac{1}{\left|{\displaystyle \sum _{i=0}^M}{\hat{a}}_i{\gamma }^i{e}^{-\mathit{ji\theta }\prime }\right|}$$

où $$\theta \prime =2\pi \frac{6000}{16000}\mathrm{.}$$

Dans un mode de réalisation privilégié, les quantités P et R sont calculées selon le pseudo-code suivant: $$\begin{array}{l}\mathit{px}=\mathit{py}=\mathit{0}\\ \mathit{rx}=\mathit{ry}=\mathit{0}\\ \mathit{for\; i}=\mathit{0}\mathit{to}\mathit{16}\\ \mathit{px}=\mathit{px}+\mathit{Ap}\left[\mathit{i}\right]*\mathit{exp\_tab\_p}\left[\mathit{i}\right]\\ \mathit{py}=\mathit{py}+\mathit{Ap}\left[\mathit{i}\right]*\mathit{exp\_tab\_}\left[\mathit{33}-\mathit{i}\right]\\ \mathit{rx}=\mathit{rx}+\mathit{Aq}\left[\mathit{i}\right]*\mathit{exp\_tab\_q}\left[\mathit{i}\right]\\ \mathit{ry}=\mathit{ry}+\mathit{Aq}\left[\mathit{i}\right]*\mathit{exp\_tab\_q}\left[\mathit{33}-\mathit{i}\right]\\ \mathit{end\; for}\\ \mathit{P}=\mathit{1}/\mathit{sqrt}\left(\mathit{px}*\mathit{px}+\mathit{py}*\mathit{py}\right)\\ \mathit{R}=\mathit{1}/\mathit{sqrt}\left(\mathit{rx}*\mathit{rx}+\mathit{ry}*\mathit{ry}\right)\end{array}$$

où Aq[i] = â_i correspond aux coefficients de Â(z) (d'ordre 16), Ap[i]= γⁱâ_i correspond aux coefficient de Â(z/γ), sqrt() correspond à l'opération de racine carrée et les tableaux exp_tab_p et exp_tab_q de taille 34 contiennent les parties réelles et imaginaires des exponentielles complexes associée à la fréquence de 6000 Hz, avec $$\mathrm{exp\_tab\_p}\left[\mathrm{i}\right]=\{\begin{array}{cc}\cos \left(2\pi \frac{6000}{12800}i\right)& i=0,\cdots ,16\\ -\sin \left(2\pi \frac{6000}{12800}\left(33-i\right)\right)& i=17,\cdots ,33\end{array}$$

$$\mathrm{exp\_tab\_q}\left[\mathrm{i}\right]=\{\begin{array}{cc}\cos \left(2\pi \frac{6000}{16000}i\right)& i=0,\cdots ,16\\ -\sin \left(2\pi \frac{6000}{16000}\left(33-i\right)\right)& i=17,\cdots ,33\end{array}$$

Le filtre de prédiction additionnel est obtenu par exemple en tronquant de façon adéquate le polynôme Â(z) à l'ordre 2.
En fait la troncature directe à l'ordre conduit au filtre 1 + â ₁ + â ₂, ce qui peut poser problème car rien ne garantit en général que ce filtre d'ordre 2 est stable. Dans un mode de réalisation privilégiée, on détecte donc la stabilité du filtre 1 + â ₁ + â ₂ et on utilise un filtre 1 + â ₁' + â ₂',
dont les coefficients sont tirés de 1 + â ₁ + â ₂ en fonction de la détection d'instabilité. Plus précisément, on initialise : $${\hat{a}}_i\prime ={\hat{a}}_i,\mathrm{i}=1,2$$

La stabilité du filtre 1 + â ₁ + â ₂ peut être vérifiée de différente façon, on utilise ici une conversion dans le domaine des coefficients PARCOR (ou coefficients de réflexion) en calculant : $$k_1={\hat{a}}_1\prime /\left(1+{\hat{a}}_2\prime \right)$$

$$k_2={\hat{a}}_2\prime$$

La stabilité est vérifiée si |k_i | < 1, i=1,2. On modifie donc de façon conditionnelle la valeur de k_i avant d'assurer la stabilité du filtre, avec les étapes suivantes : $$k_2\leftarrow \{\begin{array}{cc}\min \left(0.6,k_2\right)& k_2>0\\ \max \left(-0.6,k_2\right)& k_2<0\end{array}$$

$$k_1\leftarrow \{\begin{array}{cc}\min \left(0.99,k_2\right)& k_1>0\\ \max \left(-0.99,k_2\right)& k_1<0\end{array}$$

où min(.,.) et max(.,.) donnent respectivement le minimum et le maximum de 2 opérandes. On note que les valeurs de seuils, 0.99 pour k ₁ et 0.6 pour k₂ , pourront être ajustées dans des variantes de l'invention. On rappelle que le premier coefficient de réflexion, k ₁, caractérise la pente spectrale (ou tilt) du signal modélisé à l'ordre 1 ; dans l'invention on sature la valeur de k ₁ à une valeur proche de la limite de stabilité, afin de préserver cette pente et conserver un tilt similaire à celui de 1/Â(z). On rappelle aussi que le second coefficient de réflexion, k ₂, caractérise le niveau de résonance du modèle de signal à l'ordre 2 ; puisque l'utilisation d'un filtre d'ordre 2 vise à éliminer l'influence de telles résonances autour de la fréquence de 6000 Hz, on limite plus fortement la valeur de k ₂, cette limite est fixée à 0.6.
Les coefficients de 1 + â ₁' + â ₂' sont alors obtenus par: $${\hat{a}}_1\prime =\left(1+k_2\right)k_1$$

$${\hat{a}}_2\prime =k_2$$

On calcule donc finalement la réponse en fréquence du filtre additionnel: $$Q=\frac{1}{\left|{\displaystyle \sum _{k=0}^2}{\hat{a}}_k\prime e^{-\mathit{jk\theta }}\right|}$$

avec $\theta =2\pi \frac{6000}{12800}\mathrm{.}$

Cette quantité est calculée de façon préférentielle selon le pseudo-code 12800 suivant : $$\begin{array}{l}\mathit{qx}=\mathit{qy}=\mathit{0}\\ \mathit{for\; i}=\mathit{0}\mathit{to}\mathit{2}\\ \mathit{qx}=\mathit{qx}+\mathit{As}\left[\mathit{i}\right]*\mathit{exp\_tab\_q}\left[\mathit{i}\right];\\ \mathit{qy}=\mathit{qy}+\mathit{As}\left[\mathit{i}\right]*\mathit{exp\_tab\_q}\left[\mathit{33}-\mathit{i}\right];\\ \mathit{end\; for}\\ \mathit{Q}=\mathit{1}/\mathit{sqrt}\left(\mathit{qx}*\mathit{qx}+\mathit{qy}*\mathit{qy}\right)\end{array}$$

où As[i] = â_i '.
Sans perte de généralité, on pourra calculer les coefficients du filtre d'ordre 2 autrement, par exemple en appliquant au filtre LPC Â(z) d'ordre 16 la procédure de réduction de l'ordre LPC dite « STEP DOWN » décrite dans J.D. Markel and A.H. Gray, Linear Prediction of Speech, Springer Verlag, 1976 ou en effectuant deux itérations d'algorithme de Levinson-Durbin (ou STEP-UP) à partir des autocorrélations calculées sur le signal synthétisé (décodé) à 12.8 kHz et fenêtré.
Pour certains signaux, la quantité Q, calculée à partir des 3 premiers coefficients LPC décodés, prend mieux en compte l'influence de la pente spectrale (ou tilt) dans le spectre et évite l'influence de pics ou de vallées « parasites » proches de 6000 Hz qui peuvent biaiser ou élever la valeur de la quantité R, calculée à partir de tous les coefficients LPC.
Dans un mode de réalisation privilégié, le facteur d'échelle optimisé est déduit des quantités pré-calculées R, P, Q de façon conditionnelle, comme suit :

• Si le tilt (calculé comme dans AMR-WB dans le bloc 104, par autocorrélation normalisée sous la forme r(1)/r(0) où r(i) est l'autocorrélation) est négatif (tilt <0 comme représenté à la figure 5b), le calcul du facteur d'échelle se fait de la façon suivante:
  • Pour éviter des artefacts dus à des variations trop brusques d'énergie de la bande haute, on applique un lissage à la valeur de R . Dans un mode de réalisation privilégié, un lissage exponentiel est effectué avec un facteur fixe dans le temps (0.5) sous la forme : $$R=0.5R+0.5R_{\mathit{prev}}$$
    
    $$R_{\mathit{prev}}=R$$
    
    où R_prev correspond à la valeur de R dans la sous-trame précédente et le facteur 0.5 est optimisé de façon empirique - bien entendu, le facteur 0.5 pourra être changé pour une autre valeur et d'autres méthodes de lissage sont également possibles. A noter que le lissage permet de réduire les variantes temporelles et évite donc des artéfacts.

Le facteur d'échelle optimisé est alors donné par : $$g_{\mathit{HB}2}\left(m\right)=\max \left(\min \left(R,Q\right),P\right)/P$$

Dans un mode de réalisation alternative, on pourra remplacer le lissage de R par un lissage de g _HB2(m) tel que: $$g_{\mathit{HB}2}\left(m\right)\leftarrow 0.5g_{\mathit{HB}2}\left(m\right)+0.5g_{\mathit{HB}2}\left(m-1\right)$$

Si le tilt (calculé comme dans AMR-WB dans le bloc 104) est positif (tilt>0 comme à la figure 5a), le calcul du facteur d'échelle se fait de la façon suivante:

• La quantité R est lissée de façon adaptative dans le temps, avec un lissage plus fort quand R est faible - comme dans le cas précédent, ce lissage permet de réduire les variantes temporelles et évite donc des artéfacts: $$R=\left(1-\alpha \right)R+{\mathit{\alpha R}}_{\mathit{prev}}\mathrm{avec}\alpha =1-R^2$$
  
  $$R_{\mathit{prev}}=R$$
  
  Ensuite, le facteur d'échelle optimisé est donné par : $$g_{\mathit{HB}2}\left(m\right)=\min \left(R,P,Q\right)/P$$
  

Dans un mode de réalisation alternative, on pourra remplacer le lissage de R par un lissage de g _HB2(m) tel que calculé ci-dessus. $$g_{\mathit{HB}}\left(m\right)=\left(1-\alpha \right)g_{\mathit{HB}}\left(m\right)+{\mathit{\alpha g}}_{\mathit{HB}}\left(m-1\right),\mathit{m}=0,\dots ,3,\mathit{\alpha }=1-g_{\mathit{HB}}^2\left(m\right)$$

ou g_HB (-1) est le facteur d'échelle ou gain calculé pour la dernière sous-trame de la trame précédente.
On prend ici le minimum de R, P, Q afin d'éviter de surestimer le facteur d'échelle.
Dans une variante, la condition ci-dessus dépendant uniquement du tilt pourra être étendue pour tenir compte non seulement du paramètre de tilt mais également d'autres paramètres afin d'affiner la décision. De plus, le calcul de g _HB2(m) pourra être ajusté en fonction de ces dits paramètres supplémentaires.
Un exemple de paramètre supplémentaire est le nombre de passage par zéro (ZCR, zero crossing rate) qui peut être défini comme : $${\mathit{zcr}}_c=\frac{1}{2}{\displaystyle \sum _{n=1}^{N-1}}\left|\mathrm{sgn}\left[s\left(n\right)\right]-\mathrm{sgn}\left(n-1\right)\right|$$

où $$\mathrm{sgn}\left(x\right)=\{\begin{array}{cc}1& \mathit{if}x\ge 0\\ -1& \mathit{if}x<0\end{array}$$

Le paramètre zcr donne généralement les résultats similaires au tilt. Un bon critère de classification est le ratio entre zcr_s calculé pour le signal synthétisé s(n) et zcr_u calculé pour le signal d'excitation u(n) à 12800 Hz. Ce ratio est entre 0 et 1, où 0 signifie que le signal a un spectre décroissant, 1 que le spectre est croissant (ce qui correspond à (1 - tilt)/2. Dans ce cas, un ratio zcr_s / zcr_u >0.5 correspond au cas tilt <0, un ratio zcr_s / zcr_u <0.5 correspond à tilt >0.
Dans une variante, on pourra utiliser une fonction d'un paramètre tilt_hp où tilt_hp est le tilt calculé pour le signal synthétisé s(n) filtré par un filtre passe haut avec une fréquence de coupure par exemple à 4800 Hz ; dans ce cas, la réponse 1/Â(z/γ) de 6 à 8 kHz (appliquée à 16 kHz) correspond à la réponse pondérée de 1/Â(z) de 4.8 à 6.4 kHz. Comme 1/Â(z/γ) a une réponse plus aplatie, il faut compenser ce changement de tilt. La fonction de facteur d'échelle selon tilt_hp est alors donnée dans un mode de réalisation par : (1 - tilt_hp )² + 0.6. On multiplie donc Q et R par min(1,(1 - tilt_hP )² + 0.6) quand tilt >0
ou par max(1,(1 - tilt_hp )² + 0.6 quand tilt <0.The principle of determining the optimized scaling factor implemented in block 401 is illustrated in FIGS. Figures 5a and 5b with concrete examples obtained from signals sampled at 16 kHz; the amplitude values of frequency responses, noted later R, P, Q, of 3 filters are calculated at the common frequency of 6000 Hz (vertical dashed line) in the current subframe, whose index m n This is not recalled here in the notation of LPC filters interpolated by sub-frame to lighten the text. The value of 6000 Hz is chosen so that it is close to the Nyquist frequency of the low band, ie 6400 Hz. It is preferable not to take this Nyquist frequency to determine the optimized scale factor. Indeed, the energy of the decoded signal at low frequencies is typically already attenuated at 6400 Hz. In addition, the band extension described here is performed on a second so-called high band frequency band which ranges from 6000 to 8000 Hz. It should be noted that in variants of the invention, another frequency than 6000 Hz may be chosen, without loss of generality in order to determine the optimized scaling factor. . We can also consider the case where the two LPC filters are defined for separate bands (as in AMR-WB +). In this case R, P and Q will be calculated at the separation frequency.
The Figures 5a and 5b illustrate how the quantities R, P, Q are defined
The first step is to calculate the R and P frequency responses respectively of the linear prediction filter of the first frequency band (low band) and the second frequency band (high band) at the frequency of 6000 Hz. 'on board : $$R=\frac{1}{\left|\widehat{\mathrm{AT}}\left(e^{\mathit{j\theta }}\right)\right|}=\frac{1}{\left|{\displaystyle \underset{i=0}{\overset{M}{\Sigma }}}{\widehat{\mathrm{at}}}_i{e}^{-\mathit{ji\theta }}\right|}$$

where M = 16 is the order of the decoded LPC filter 1 / Â ( z ), and θ corresponds to the normalized 6000 Hz frequency for the sampling frequency of 12.8 kHz, that is: $$\theta =2\pi \frac{6000}{12800}\mathrm{.}$$

Then, similarly, we calculate: $$P=\frac{1}{\left|\widehat{\mathrm{AT}}\left(e^{\mathit{j\theta }\text{'}}/\gamma \right)\right|}=\frac{1}{\left|{\displaystyle \underset{i=0}{\overset{M}{\Sigma }}}{\widehat{\mathrm{at}}}_i{\gamma }^i{e}^{-\mathit{ji\theta }\text{'}}\right|}$$

or $$\theta \text{'}=2\pi \frac{6000}{16000}\mathrm{.}$$

In a preferred embodiment, the quantities P and R are calculated according to the following pseudo-code: $$\begin{array}{l}\mathit{px}=\mathit{py}=\mathit{0}\\ \mathit{rx}=\mathit{ry}=\mathit{0}\\ \mathit{for\; i}=\mathit{0}\mathit{to}\mathit{16}\\ \mathit{px}=\mathit{px}+\mathit{Ap}\left[\mathit{i}\right]*\mathit{exp\_tab\_p}\left[\mathit{i}\right]\\ \mathit{py}=\mathit{py}+\mathit{Ap}\left[\mathit{i}\right]*\mathit{exp\_tab\_}\left[\mathit{33}-\mathit{i}\right]\\ \mathit{rx}=\mathit{rx}+\mathit{Aq}\left[\mathit{i}\right]*\mathit{exp\_tab\_q}\left[\mathit{i}\right]\\ \mathit{ry}=\mathit{ry}+\mathit{Aq}\left[\mathit{i}\right]*\mathit{exp\_tab\_q}\left[\mathit{33}-\mathit{i}\right]\\ \mathit{end\; for}\\ \mathit{P}=\mathit{1}/\mathit{sqrt}\left(\mathit{px}*\mathit{px}+\mathit{py}*\mathit{py}\right)\\ \mathit{R}=\mathit{1}/\mathit{sqrt}\left(\mathit{rx}*\mathit{rx}+\mathit{ry}*\mathit{ry}\right)\end{array}$$

where Aq [i] = a _i corresponds to the coefficients of  (z) (of order 16), Rv [i] = γ ⁱ â _i is the coefficient of A (z / γ), sqrt () is the square root operation and tables exp_tab_p and exp_tab_q of size 34 contain the real and imaginary parts of complex exponentials associated with the frequency of 6000 Hz, with $$\mathrm{exp\_tab\_p}\left[\mathrm{i}\right]=\{\begin{array}{cc}\cos \left(2\pi \frac{6000}{12800}i\right)& i=0,\cdots ,16\\ -\sin \left(2\pi \frac{6000}{12800}\left(33-i\right)\right)& i=17,\cdots ,33\end{array}$$

$$\mathrm{exp\_tab\_q}\left[\mathrm{i}\right]=\{\begin{array}{cc}\cos \left(2\pi \frac{6000}{16000}i\right)& i=0,\cdots ,16\\ -\sin \left(2\pi \frac{6000}{16000}\left(33-i\right)\right)& i=17,\cdots ,33\end{array}$$

The additional prediction filter is obtained for example by appropriately truncating the polynomial  (z) to order 2.
In fact the direct truncation order led to the filter + 1 to ₁ + to _2, which can be a problem because there is no guarantee that in general order filter 2 is stable. In one preferred embodiment, thus detecting the stability of the filter 1 + a ₁ + a ₂ and a filter are used 1 + a ₁ '+ a _2',
whose coefficients are derived from a 1 + a ₁ + a ₂ as a function of the detection of instability. More precisely, we initialize: $${\widehat{\mathrm{at}}}_i\text{'}={\widehat{\mathrm{at}}}_i,\mathrm{i}=1,2$$

The stability of the filter 1 + a ₁ + a ₂ can be checked in different ways, by using a conversion in the field of PARCOR coefficients (or reflection coefficients) by calculating: $${\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}_1={\widehat{\mathrm{at}}}_1\text{'}/\left(1+{\widehat{\mathrm{at}}}_2\text{'}\right)$$

$${\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}}_2={\widehat{\mathrm{at}}}_2\text{'}$$

Stability is verified if | k _i | <1, i = 1.2. The value of k _{i is then} conditionally modified before ensuring the stability of the filter, with the following steps: $${\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}}_2\leftarrow \{\begin{array}{cc}\min \left(0.6,k_2\right)& {\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}}_2>0\\ \max \left(-0.6,k_2\right)& {\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}}_2<0\end{array}$$

$${\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}_1\leftarrow \{\begin{array}{cc}\min \left(0.99,k_2\right)& {\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}_1>0\\ \max \left(-0.99,k_2\right)& {\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}_1<0\end{array}$$

where min (.,.) and max (.,.) respectively give the minimum and maximum of 2 operands. It is noted that the threshold values, 0.99 for k ₁ and 0.6 for k ₂ , may be adjusted in variants of the invention. It is recalled that the first reflection coefficient, k ₁ , characterizes the spectral slope (or tilt) of the signal modeled at the order 1; in the invention is saturated value of k ₁ to a value close to the limit of stability in order to maintain the slope and maintain a tilt similar to that of 1 / Â (z). It is also recalled that the second reflection coefficient, k ₂ , characterizes the resonance level of the signal model at order 2; since the use of a filter of order 2 aims at eliminating the influence of such resonances around the frequency of 6000 Hz, the value of k ₂ is more strongly limited, this limit is fixed at 0.6.
The coefficients of + 1 to ₁ '+ to _2' are then obtained by: $${\widehat{\mathrm{at}}}_1\text{'}=\left(1+k_2\right){\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}_1$$

$${\widehat{\mathrm{at}}}_2\text{'}={\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}}_2$$

Finally, the frequency response of the additional filter is calculated: $$Q=\frac{1}{\left|{\displaystyle \underset{k=0}{\overset{2}{\Sigma }}}{\widehat{\mathrm{at}}}_k\text{'}{e}^{-\mathit{jk\theta }}\right|}$$

with $\theta =2\pi \frac{6000}{12800}\mathrm{.}$

This quantity is preferably calculated according to the following pseudo-code 12800: $$\begin{array}{l}\mathit{quintals}=\mathit{qy}=\mathit{0}\\ \mathit{for\; i}=\mathit{0}\mathit{to}\mathit{2}\\ \mathit{quintals}=\mathit{quintals}+\mathit{ace}\left[\mathit{i}\right]*\mathit{exp\_tab\_q}\left[\mathit{i}\right];\\ \mathit{qy}=\mathit{qy}+\mathit{ace}\left[\mathit{i}\right]*\mathit{exp\_tab\_q}\left[\mathit{33}-\mathit{i}\right];\\ \mathit{end\; for}\\ \mathit{Q}=\mathit{1}/\mathit{sqrt}\left(\mathit{quintals}*\mathit{quintals}+\mathit{qy}*\mathit{qy}\right)\end{array}$$

where As [i] = a _i '.
Without loss of generality, we can calculate the order of filter coefficients 2 otherwise, for example by applying LPC filter  (z) of order 16 the procedure of reducing the order LPC called "STEP DOWN" described in JD Markel and AH Gray, Linear Prediction of Speech, Springer Verlag, 1976 or by performing two Levinson-Durbin (or STEP-UP) algorithm iterations from the autocorrelations calculated on the synthesized (decoded) signal at 12.8 kHz and windowed.
For some signals, the quantity Q , calculated from the first 3 decoded LPC coefficients, takes better account of the influence of the spectral slope (or tilt) in the spectrum and avoids the influence of nearby "parasitic" peaks or valleys 6000 Hz which can bias or raise the value of the quantity R , calculated from all the LPC coefficients.
In a preferred embodiment, the optimized scaling factor is derived from the precalculated quantities R, P, Q conditionally as follows:

• If the tilt (calculated as in AMR-WB in block 104, by normalized autocorrelation in the form r (1) / r (0) where r (i) is autocorrelation) is negative (tilt <0 as shown in FIG. figure 5b ), the calculation of the scale factor is as follows:
  • To avoid artefacts due to abrupt changes in energy of the high band, a smoothing is applied to the value of R. In a preferred embodiment, an exponential smoothing is performed with a fixed factor in time (0.5) in the form: $$R=0.5R+0.5R_{\mathit{prev}}$$
    
    $$R_{\mathit{prev}}=R$$
    
    where R _prev corresponds to the value of R in the preceding sub-frame and the factor 0.5 is optimized empirically - of course, the factor 0.5 can be changed to another value and other smoothing methods are also possible. Note that smoothing reduces temporal variations and therefore avoids artifacts.

The optimized scale factor is then given by: $${\mathrm{boy\; Wut}}_{\mathit{HB}2}\left(m\right)=\max \left(\min \left(R,Q\right),P\right)/P$$

In an alternative embodiment, it is possible to replace the smoothing of R by a smoothing of g _{HB 2} ( m ) such that: $${\mathrm{boy\; Wut}}_{\mathit{HB}2}\left(m\right)\leftarrow 0.5{\mathrm{boy\; Wut}}_{\mathit{HB}2}\left(m\right)+0.5{\mathrm{boy\; Wut}}_{\mathit{HB}2}\left(m-1\right)$$

If the tilt (calculated as in AMR-WB in block 104) is positive (tilt> 0 as in figure 5a ), the calculation of the scale factor is as follows:

• The quantity R is smoothed adaptively over time, with a stronger smoothing when R is weak - as in the previous case, this smoothing makes it possible to reduce the temporal variants and thus avoids artifacts: $$R=\left(1-\alpha \right)R+{\mathit{\alpha R}}_{\mathit{prev}}\mathrm{with}\alpha =1-R^2$$
  
  $$R_{\mathit{prev}}=R$$
  
  Then the optimized scaling factor is given by: $${\mathrm{boy\; Wut}}_{\mathit{HB}2}\left(m\right)=\min \left(R,P,Q\right)/P$$
  

In an alternative embodiment, can be replaced by R smoothing a smoothing _HB g ₂ (m) as calculated above. $${\mathrm{boy\; Wut}}_{\mathit{HB}}\left(m\right)=\left(1-\alpha \right){\mathrm{boy\; Wut}}_{\mathit{HB}}\left(m\right)+{\mathit{\alpha g}}_{\mathit{HB}}\left(m-1\right),\mathit{m}=0,...,3,\mathit{\alpha }=1-{\mathrm{boy\; Wut}}_{\mathit{HB}}^2\left(m\right)$$

or g _HB (-1) is the scale factor or gain calculated for the last subframe of the previous frame.
Here we take the minimum of R, P, Q in order to avoid overestimating the scale factor.
Alternatively, the above tilt-only condition may be extended to take into account not only the tilt parameter but also other parameters to refine the decision. In addition, the calculation of g _{HB 2} ( m ) can be adjusted according to these additional parameters.
An example of an additional parameter is the zero crossing rate (ZCR) which can be defined as: $${\mathit{ZCR}}_{\mathrm{vs}}=\frac{1}{2}{\displaystyle \underset{\mathrm{not}=1}{\overset{\mathrm{NOT}-1}{\Sigma }}}\left|\mathrm{sgn}\left[s\left(\mathrm{not}\right)\right]-\mathrm{sgn}\left(\mathrm{not}-1\right)\right|$$

or $$\mathrm{sgn}\left(x\right)=\{\begin{array}{cc}1& \mathit{yew}x\ge 0\\ -1& \mathit{yew}x<0\end{array}$$

The zcr parameter usually gives the results similar to the tilt. A good classification criterion is the ratio between zcr _s calculated for the synthesized signal s (n) and zcr _u calculated for the excitation signal u ( n ) at 12800 Hz. This ratio is between 0 and 1, where 0 means that the signal has a decreasing spectrum, 1 that the spectrum is increasing (corresponding to (1 - tilt) / 2 in this case, a ratio ZCR _s / ZCR _u> 0.5 corresponds to the case tilt <0, a ratio ZCR _s. / zcr _u <0.5 corresponds to tilt > 0.
In a variant, it is possible to use a function of a parameter tilt _hp where tilt _hp is the tilt calculated for the synthesized signal s ( n ) filtered by a high-pass filter with a cut-off frequency, for example at 4800 Hz; in this case, the 1 / Â (z / γ ) response of 6 to 8 kHz (applied at 16 kHz) corresponds to the weighted response of 1 / Â (z) from 4.8 to 6.4 kHz. Since 1 / Â (z / γ ) has a more flattened response, you have to compensate for this change in tilt. Function The scale factor according to tilt _hp is then given in one embodiment by: (1 - tilt _hp ) ² + 0.6. We then multiply Q and R by min (1, (1 - tilt _hP ) ² + 0.6) when tilt > 0
or by max (1, (1 - tilt _hp ) ² + 0.6 when tilt <0.

Pour pouvoir appliquer l'information de gain reçue à 23.85 kbit/s (dans le bloc 407), il est important de ramener l'excitation à un niveau similaire à celui attendu au codage (compatible) AMR-WB. Ainsi, le bloc 404 effectue la mise à l'échelle du signal d'excitation selon l'équation suivante: $$u_{\mathit{HB}1}\left(n\right)=g_{\mathit{HB}3}\left(m\right)u_{\mathit{HB}}\left(n\right),n=80m,\cdots ,80\left(m+1\right)-1$$

où g_HB3 (m) est un gain par sous-trame calculé dans le bloc 403 sous la forme : $$g_{\mathit{HB}3}\left(m\right)=\sqrt{\frac{{\displaystyle \sum _{n=0}^{63}}u{\left(n\right)}^2}{5.{\displaystyle \sum _{n=0}^{79}}{u}_{\mathit{HB}}{\left(n\right)}^2}}$$

où le facteur 5 au dénominateur sert à compenser la différence de largeur de bande entre le signal u(n) et le signal u_HB (n), sachant qu'au codage AMR-WB l'excitation HF est un bruit blanc sur la bande 0-8000 Hz.
L'indice de 4 bits par sous-trame, noté index_HF_g_ain(m), envoyé à 23.85 kbit/s est démultiplexé du train binaire (bloc 405) et décodé par le bloc 406 de la façon suivante : $$g_{\mathit{HBcorr}}\left(m\right)=2.\mathit{HP}\mathrm{\_gain}\left({\mathrm{index}}_{\mathrm{HP\_gain}}\left(m\right)\right)$$

où HP_gain(.) est le dictionnaire de quantification de gain HF défini dans le codage AMR-WB et rappelé ci-dessous : Tableau 1 (dictionnaire de gain à 23.85 kbit/s) i HP_gain(i) I HP_gain(i) 0 0.110595703125000 8 0.342102050781250 1 0.142608642578125 9 0.372497558593750 2 0.170806884765625 10 0.408660888671875 3 0.197723388671875 11 0.453002929687500 4 0.226593017578125 12 0.511779785156250 5 0.255676269531250 13 0.599822998046875f 6 0.284545898437500 14 0.741241455078125 7 0.313232421875000 15 0.998779296875000 Le bloc 407 effectue la mise à l'échelle du signal d'excitation selon l'équation suivante: $$u_{\mathit{HB}2}\left(n\right)=g_{\mathit{HBcorr}}\left(m\right)u_{\mathit{HB}1}\left(n\right),n=80m,\cdots ,80\left(m+1\right)-1$$

Enfin, on ajuste l'énergie de l'excitation au niveau de la sous-trame courante avec les conditions suivantes (bloc 408). On calcule : $$\mathit{fac}\left(m\right)=\sqrt{\frac{{\displaystyle \sum _{n=0}^{79}}{\left({g\left(m\right)g}_{\mathit{HB}2}\left(m\right)u_{\mathit{HB}}\left(n\right)\right)}^2}{{\displaystyle \sum _{n=0}^{79}}{u}_{\mathit{HB}2}{\left(n\right)}^2}}$$

Le numérateur représente ici l'énergie de signal bande-haute qui serait obtenue dans le mode 23.05. Comme expliqué avant, pour les débits <23.85 kbit/s il faut conserver le niveau d'énergie entre le signal d'excitation décodé et le signal d'excitation étendu u_HB (n), mais cette contrainte n'est pas nécessaire dans le cas du débit de 23.85 kbit/s, puisque u_HB (n) est dans ce cas mis à l'échelle par le gain g_HB3 (m). Pour éviter les doubles multiplications certaines opérations de multiplications appliqués au signal dans le bloc 400 sont appliquées dans le bloc 402 en multipliant par g(m). La valeur de g(m) dépend de l'algorithme de synthèse de u_HB (n) et doit être ajusté de telle sorte que le niveau d'énergie entre le signal d'excitation décodé en bande basse et le signal g(m)u_HB (n) soit conservé.
Dans un mode de réalisation particulier, qui sera décrit en détail plus tard en référence à la figure 7, g(m) = 0.6g _HB1(m), où g _HB1(m) est un gain qui assure, pour le signal u_HB, le même ratio entre énergie par sous-trame et énergie par trame que pour le signal u(n) et 0.6 correspond à la valeur moyenne d'amplitude de réponse en fréquence du filtre de désaccentuation de 5000 à 6400 Hz.
On suppose que dans le bloc 408 on dispose d'une information sur le tilt du signal bande basse - dans un mode de réalisation privilégié ce tilt est calculé comme dans le codec AMR-WB selon les blocs 103 et 104, cependant d'autres méthodes d'estimation du tilt sont possibles sans changer le principe de l'invention.
Si fac(m) >1 ou tilt <0, on prend : $$u_{\mathit{HB}}\prime \left(n\right)=u_{\mathit{HB}2}\left(n\right),n=80m,\cdots ,80\left(m+1\right)-1$$

Sinon : $$u_{\mathit{HB}}\prime \left(n\right)=\max \left(\sqrt{1-\mathrm{tilt}},\mathit{fac}\left(m\right)\right)\mathrm{.}{u}_{\mathit{HB}2}\left(n\right),n=80m,\cdots ,80\left(m+1\right)-1$$

On notera que le calcul de facteur d'échelle optimisé présenté ici, notamment dans les blocs 401 et 402, se distingue de l'égalisation précitée de niveaux de filtres effectuée dans le codec AMR-WB+ par plusieurs aspects :

• Le facteur d'échelle optimisé est calculé directement à partir des fonctions de transfert des filtres LPC sans impliquer de filtrage temporel. Ceci simplifie le procédé.
• L'égalisation est faite de préférence à une fréquence différente de la fréquence de Nyquist (6400 Hz) associée à la bande basse. En effet, la modélisation LPC représente implicitement l'atténuation du signal typiquement causée par les opérations de ré-échantillonnage et donc la réponse en fréquence d'un filtre LPC peut subir à la fréquence de Nyquist une diminution qui ne se retrouve pas à la fréquence commune choisie.
• L'égalisation repose ici sur un filtre d'ordre moins élevé (ici d'ordre 2) en plus des 2 filtres à égaliser. Ce filtre additionnel permet d'éviter les effets de fluctuations spectrales locales (pic ou vallée) qui peuvent être présentes à la fréquence commune pour le calcul de la réponse en fréquence des filtres de prédiction.

Pour les blocs 403 à 408, l'avantage de l'invention est que la qualité du signal décodé à 23.85 kbit/s selon l'invention est améliorée par rapport à un signal décodé à 23.05 kbit/s, ce qui n'est pas le cas dans un décodeur AMR-WB. En fait, cet aspect de l'invention permet d'utiliser l'information supplémentaire (0.8 kbit/s) reçue à 23.85 kbit/s, mais de façon contrôlée (bloc 408), pour améliorer la qualité du signal d'excitation étendu au débit de 23.85.
Le dispositif de détermination du facteur d'échelle optimisé tel qu'illustré par les blocs 401 à 408 de la figure 4, met en oeuvre un procédé de détermination du facteur d'échelle optimisé décrit maintenant en référence à la figure 6 .We now consider the case of the 23.85kbit / s rate, for which a gain correction is performed by the blocks 403 to 408. This gain correction could also be the subject of a separate invention. In this particular mode according to the invention, the gain correction information, denoted g _HBcorr ( m ), transmitted by the encoding (compatible) AMR-WB with a bit rate of 0.8 kbit / s is used to improve the quality at 23.85. kbit / s.
It is assumed here that the (compatible) AMR-WB encoding performed 4-bit correction gain quantization as described in clause ITU-T G.722.2 / 5.11 or equivalently in clause 3GPP TS 26.190 / 5.11.
In the AMR-WB encoder, the correction gain is calculated by comparing the energy of the sampled original signal at 16 kHz and filtered by a 6-7 kHz bandpass filter, s _HB ( n ) with white noise energy at 16 kHz filtered by a synthesis filter 1 / Â ( z / γ ) and a 6-7 kHz bandpass filter (before filtering the noise energy is set to a level similar to that of the 12.8 excitation) kHz), s _{HB 2} ( n ). The gain is the root of the energy ratio of the original signal on the energy of the noise divided by two. In a possible embodiment, the bandpass filter can be changed for a filter with a wider band (for example from 6 to 7.6 kHz). $${\mathrm{boy\; Wut}}_{\mathit{HBcorr}}\left(m\right)=\sqrt{\frac{{\displaystyle \underset{\mathrm{not}=80m}{\overset{80\left(m+1\right)-1}{\Sigma }}}{s}_{\mathit{HB}}{\left(\mathrm{not}\right)}^2}{{\displaystyle \underset{\mathrm{not}=80m}{\overset{80\left(m+1\right)-1}{\Sigma }}}{s}_{\mathit{<figure-callout\; id="2"\; label="HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">HB</figure-callout>}2}{\left(\mathrm{not}\right)}^2}},\mathit{m}=0,...,3$$

In order to be able to apply the received gain information at 23.85 kbit / s (in block 407), it is important to reduce the excitation to a level similar to that expected at AMR-WB (compatible) coding. Thus, block 404 scales the excitation signal according to the following equation: $${\mathrm{<figure-callout\; id="1"\; label="u\; HB"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}\left(\mathrm{not}\right)={\mathrm{boy\; Wut}}_{\mathit{HB}3}\left(m\right)u_{\mathit{HB}}\left(\mathrm{not}\right),\mathrm{not}=80m,\cdots ,80\left(m+1\right)-1$$

where g _HB3 ( m ) is a subframe gain calculated in block 403 in the form: $${\mathrm{boy\; Wut}}_{\mathit{HB}3}\left(m\right)=\sqrt{\frac{{\displaystyle \underset{\mathrm{not}=0}{\overset{63}{\Sigma }}}u{\left(\mathrm{not}\right)}^2}{5.{\displaystyle \underset{\mathrm{not}=0}{\overset{79}{\Sigma }}}{u}_{\mathit{HB}}{\left(\mathrm{not}\right)}^2}}$$

where the factor 5 at the denominator serves to compensate for the difference in bandwidth between the signal u ( n ) and the signal u _HB ( n ), knowing that at the AMR-WB coding the HF excitation is a white noise on the band 0-8000 Hz.
The index of 4 bits per subframe, denoted _HF index _g _ain ( m ), sent at 23.85 kbit / s is demultiplexed from the bitstream (block 405) and decoded by block 406 as follows: $${\mathrm{boy\; Wut}}_{\mathit{HBcorr}}\left(m\right)=2.\mathit{HP}\mathrm{\_gain}\left({\mathrm{index}}_{\mathrm{HP\_gain}}\left(m\right)\right)$$

where HP _gain (.) is the HF gain quantization dictionary defined in the AMR-WB encoding and recalled below: <b> Table 1 (23.85 kbit / s gain dictionary) </ b> i HP_gain ( i ) I HP_gain ( i ) 0 0.110595703125000 8 0.342102050781250 1 0.142608642578125 9 0.372497558593750 2 0.170806884765625 10 0.408660888671875 3 0.197723388671875 11 0.453002929687500 4 0.226593017578125 12 0.511779785156250 5 0.255676269531250 13 0.599822998046875f 6 0.284545898437500 14 0.741241455078125 7 0.313232421875000 15 0.998779296875000 Block 407 scales the excitation signal according to the following equation: $${\mathrm{<figure-callout\; id="2"\; label="u\; HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}\left(\mathrm{not}\right)={\mathrm{boy\; Wut}}_{\mathit{HBcorr}}\left(\mathrm{<figure-callout\; id="1"\; label="m\; u\; HB"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">m\; </figure-callout>},\right)u_{\mathit{HB}}{\mathit{}1}_{}\left(\mathrm{not}\right),\mathrm{not}=80m,\cdots ,80\left(m+1\right)-1$$

Finally, the excitation energy is adjusted at the level of the current subframe with the following conditions (block 408). We calculate: $$\mathit{uni}\left(m\right)=\sqrt{\frac{{\displaystyle \underset{\mathrm{not}=0}{\overset{79}{\Sigma }}}{\left({\mathrm{boy\; Wut}\left(m\right)\mathrm{boy\; Wut}}_{\mathit{HB}2}\left(m\right)u_{\mathit{HB}}\left(\mathrm{not}\right)\right)}^2}{{\displaystyle \underset{\mathrm{not}=0}{\overset{79}{\Sigma }}}{\mathrm{<figure-callout\; id="2"\; label="u\; HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}{\left(\mathrm{not}\right)}^2}}$$

The numerator represents here the band-high signal energy that would be obtained in the 23.05 mode. As explained above, for rates <23.85 kbit / s the energy level between the decoded excitation signal and the extended excitation signal u _HB ( n ) must be maintained, but this constraint is not necessary in the case of the 23.85 kbit / s rate, since u _HB ( n ) is in this case scaled by the gain g _HB3 ( m ). To avoid double multiplications, certain multiplication operations applied to the signal in block 400 are applied in block 402 by multiplying by g ( m ). The value of g ( m ) depends on the algorithm of synthesis of u _HB ( n ) and must be adjusted so that the energy level between the decoded low band excitation signal and the g ( m ) u _HB ( n ) signal is conserved.
In a particular embodiment, which will be described in detail later with reference to the figure 7 , g ( m ) = 0.6 g _{HB 1} ( m ), where g _{HB 1} ( m ) is a gain which provides, for the signal u _HB , the same ratio of energy per subframe and energy per frame as for the signal u ( n ) and 0.6 is the mean value of frequency response amplitude of the deemphasis filter from 5000 to 6400 Hz.
It is assumed that in block 408 there is information on the tilt of the low band signal - in a preferred embodiment this tilt is calculated as in the AMR-WB codec according to blocks 103 and 104, however other methods tilt estimation are possible without changing the principle of the invention.
If fac ( m )> 1 or tilt <0, we take: $$u_{\mathit{HB}}\text{'}\left(\mathrm{not}\right)={\mathrm{<figure-callout\; id="2"\; label="u\; HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}\left(\mathrm{not}\right),\mathrm{not}=80m,\cdots ,80\left(m+1\right)-1$$

If not : $$u_{\mathit{HB}}\text{'}\left(\mathrm{not}\right)=\max \left(\sqrt{1-\mathrm{tilt}},\mathit{uni}\left(m\right)\right)\mathrm{.}{\mathrm{<figure-callout\; id="2"\; label="u\; HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}\left(\mathrm{not}\right),\mathrm{not}=80m,\cdots ,80\left(m+1\right)-1$$

It should be noted that the optimized scale factor calculation presented here, in particular in blocks 401 and 402, differs from the aforementioned equalization of filter levels performed in the AMR-WB + codec by several aspects:

• The optimized scaling factor is calculated directly from the transfer functions of the LPC filters without involving temporal filtering. This simplifies the process.
• The equalization is preferably done at a frequency different from the Nyquist frequency (6400 Hz) associated with the low band. Indeed, the LPC model implicitly represents the attenuation of the signal typically caused by resampling operations and therefore the frequency response of an LPC filter can undergo a decrease at the Nyquist frequency which is not found at the frequency chosen commune.
• The equalization here is based on a lower order filter (here of order 2) in addition to the 2 filters to equalize. This additional filter makes it possible to avoid the effects of local spectral fluctuations (peak or valley) that may be present at the common frequency for calculating the frequency response of the prediction filters.

For the blocks 403 to 408, the advantage of the invention is that the quality of the decoded signal at 23.85 kbit / s according to the invention is improved compared to a signal decoded at 23.05 kbit / s, which is not the case in an AMR-WB decoder. In fact, this aspect of the invention makes it possible to use the additional information (0.8 kbit / s) received at 23.85 kbit / s, but in a controlled manner (block 408), to improve the quality of the excitation signal extended to flow rate of 23.85.
The device for determining the optimized scale factor as illustrated by blocks 401 to 408 of FIG. figure 4 , implements a method of determining the optimized scale factor described now with reference to the figure 6 .

The main steps are implemented by block 401.

Thus, an extended excitation signal u _HB (n) is obtained during a frequency band extension method E601 which comprises a decoding or extraction step, in a first so-called low band frequency band, an excitation signal and parameters of the first frequency band, for example the coefficients of the linear prediction filter of the first frequency band.

A step E602 determines a linear prediction filter called additional filter, of a lower order than that of the first frequency band. To determine this filter, the parameters of the first decoded or extracted frequency band are used.

In one embodiment, this step is performed by truncation of the transfer function of the linear prediction filter of the low band to obtain a lower filter order, for example 2. These coefficients can then be modified according to a criterion of stability as explained above with reference to the figure 4 .

From the coefficients of the additional filter thus determined, a step E603 is implemented to calculate the optimized scale factor to be applied to the extended excitation signal. This optimized scale factor is for example calculated from the frequency response of the additional filter at a common frequency between the low band (first frequency band) and the high band (second frequency band). A minimum value that can be chosen between the frequency response of this filter and those of the low band and high band filters.
This avoids the overestimation of energy that could exist in state-of-the-art methods.

This step of calculating the optimized scale factor is for example described above with reference to the figure 4 and to Figures 5a and 5b .

Step E604 performed by block 402 or 409 (depending on the decoding rate) for the band extension, applies the optimized scaling factor thus calculated to the extended excitation signal so as to obtain an extended excitation signal. optimized u _HB '( n ).

In a particular embodiment, the optimized scaling factor device 708 is integrated in a tape expansion device described now with reference to the figure 7 . This optimized scale factor determination device illustrated by block 708 implements the method of determining the optimized scale factor described above with reference to FIG. figure 6 .

In this embodiment, the band extension block 400 of the figure 4 includes blocks 700 to 707 of the figure 7 described now.

Thus, at the input of the band extender, a decoded or analytically estimated low band excitation signal is received ( u ( n )). The band extension here uses the decoded excitation at 12.8 kHz (exc2 or u ( n )) at the output of the block 302 of the figure 3 .

Note that in this embodiment, the generation of the oversampled and extended excitation is carried out in a frequency band ranging from 5 to 8 kHz including a second frequency band (6.4-8kHz) greater than the first band of frequency (0-6.4 kHz).

Thus, the generation of an extended excitation signal is effected at least on the second frequency band but also on a part of the first frequency band.

Of course, the values defining these frequency bands may be different depending on the decoder or the processing device in which the invention applies.

où N = 256 et k = 0, ..., 255.
On note ici que la transformation sans fenêtrage (ou de façon équivalente avec une fenêtre rectangulaire implicite de la longueur de la trame) est possible car le traitement est effectué dans le domaine de l'excitation, et non le domaine du signal, si bien qu'aucun artefact (effets de bloc) n'est audible, ce qui constitue un avantage important de ce mode de réalisation de l'invention.For this exemplary embodiment, this signal is transformed to obtain an excitation signal spectrum U ( k ) by the time-frequency transformation module 500.
In a particular embodiment, the transform uses a DCT-IV (for "Discrete Cosine Transform" - Type IV in English) (block 700) on the current frame of 20 ms (256 samples), without windowing, which amounts to directly transform u ( n ) with n = 0, ..., 255 according to the following formula: $$U\left(k\right)={\displaystyle \underset{\mathrm{not}=0}{\overset{\mathrm{NOT}-1}{\Sigma }}}u\left(\mathrm{not}\right)\cos \left(\frac{\pi }{\mathrm{NOT}}\left(\mathrm{not}+\frac{1}{2}\right)\left(k+\frac{1}{2}\right)\right)$$

where N = 256 and k = 0, ..., 255.
We note here that the transformation without windowing (or equivalently with a rectangular window implicit in the length of the frame) is possible because the processing is performed in the field of excitation, and not the domain of the signal, so that no artifact (block effects) is audible, which is an important advantage of this embodiment of the invention.

In this embodiment, the DCT-IV transformation is implemented by FFT according to the algorithm called " Evolved DCT (EDCT)" described in the article by DM Zhang, HT Li, A Low Complexity Transform - Evolved DCT, IEEE 14th International Conference on Computational Science and Engineering (CSE), Aug. 2011, pp. 144-149 , and implemented in ITU-T G.718 Annex B and G.729.1 Annex E.

In variants of the invention and without loss of generality, the DCT-IV transformation may be replaced with other short-term time-frequency transformations of the same length and in the field of excitation, such as an FFT (for " Fast Fourier Transform "in English ) or DCT-II ( Discrete Cosine Transform - Type II). Alternatively, we can replace the DCT-IV on the frame by a recovery-addition and windowing transformation of length greater than the length of the frame current, for example using an MDCT (for "Modified Discrete Cosine Tranform" in English). In this case the delay T in the block 310 of the figure 3 , should be adjusted (reduced) adequately according to the additional delay due to the analysis / synthesis by this transform.

où on prend de façon préférentielle start_band = 160.The DCT spectrum, U ( k ), of 256 samples covering the band 0-6400 Hz (at 12.8 kHz), is then extended (block 701) into a spectrum of 320 samples covering the band 0-8000 Hz (at 16 kHz) in the following form: $$U_{\mathit{HB}1}\left(k\right)=\{\begin{array}{cc}0\hfill & k=0,\cdots ,199\hfill \\ U\left(k\right)\hfill & k=200,\cdots ,239\hfill \\ U\left(k+\mathit{start\_band}-240\right)& k=240,\cdots ,319\hfill \end{array}$$

where it is preferential to start _ band = 160.

The block 701 functions as a module for generating an oversampled and extended excitation signal and performs a resampling of 12.8 to 16 kHz in the frequency domain, by adding ¼ samples ( k = 240, ... , 319) to the spectrum, the ratio between 16 and 12.8 being 5/4.

In addition, block 701 performs high pass filtering implicit in the 0-5000 Hz band since the first 200 samples of U _{HB 1} ( k ) are set to zero; as explained later, this high-pass filtering is also completed by a progressive attenuation part of the spectral values of indices k = 200,..., 255 in the band 5000-6400 Hz, this progressive attenuation is implemented in the block 704 but could be carried out separately outside the block 704. Equivalently and in variants of the invention, the implementation of high-pass filtering separated into blocks of coefficients of index k = 0, .. ., 199, zeroed, coefficients k = 200, ..., 255 attenuated, in the transformed domain, can therefore be performed in a single step.

In this exemplary embodiment and according to the definition of U _{HE 1} ( k ), it is noted that the 5000-6000 Hz band of U _{HB 1} ( k ) (which corresponds to the indices k = 200, ..., 239) is copied from the 5000-6000 Hz U ( k ) band. This approach preserves the original spectrum in this band and avoids introducing distortions in the 5000-6000 Hz band during the addition of HF synthesis with BF synthesis - particularly the signal phase (implicitly represented in the DCT-IV domain) in this band is preserved.

The band 6000-8000 Hz of U _{HB 1} ( k ) is here defined by copying the 4000-6000 Hz band of U ( k ) since the value of start_band is preferably fixed at 160.

In a variant of the embodiment, the value of start_band can be made adaptive around the value of 160. The details of the adaptation of the value start_band are not described here because they go beyond the scope of the invention without changing the scope.

For some broadband signals (sampled at 16 kHz), the high band (> 6 kHz) may be noisy, harmonic or have a mixture of noise and harmonics. In addition, the level of harmonicity in the 6000-8000 Hz band is generally correlated with that of the lower frequency bands. Thus, the noise generation block 702 generates a noise generation in the frequency domain, U _HBN ( k ) for k = 240,..., 319 (80 samples) corresponding to a second so-called high frequency frequency band in order to then combine this noise with the spectrum U _{HB 1} ( k ) in block 703.

avec la convention que U_HBN (239) dans la trame courante correspond à la valeur U_HBN (319) de la trame précédente. Dans des variantes de l'invention, on pourra remplacer cette génération de bruit par d'autres méthodes.In a particular embodiment, the noise (in the 6000-8000 Hz band) is generated pseudo-randomly with a 16-bit linear congruent generator: $$U_{\mathit{HBN}}\left(k\right)=\{\begin{array}{cc}0\hfill & k=0,\cdots ,239\hfill \\ 31821U_{\mathit{HBN}}\left(k-1\right)+13849\hfill & k=240,\cdots ,319\hfill \end{array}$$

with the convention that U _HBN (239) in the current frame corresponds to the value U _HBN (319) of the previous frame. In variants of the invention, this noise generation can be replaced by other methods.

où G_HBN est un facteur de normalisation servant à égaliser le niveau d'énergie entre les deux signaux, $$G_{\mathit{HBN}}=\sqrt{\frac{{\displaystyle \sum _{k=240}^{319}}{U}_{\mathit{HB}1}{\left(k\right)}^2+\epsilon }{{\displaystyle \sum _{k=240}^{319}}{U}_{\mathit{HBN}}{\left(k\right)}^2+\epsilon }}$$

avec ε = 0.01, et le coefficient α (compris entre 0 et 1) est ajusté en fonction de paramètres estimés à partir de la bande basse décodée et le coefficient β (compris entre 0 et 1) dépend de α.The combination block 703 can be realized in different ways. In a privileged way, we consider an adaptive additive mix of the form: $$U_{\mathit{HB}2}\left(k\right)={\mathit{\beta U}}_{\mathit{HB}1}\left(k\right)+{\mathit{\alpha G}}_{\mathit{HBN}}{U}_{\mathit{HBN}}\left(k\right),k=240,\cdots ,319$$

where G _HBN is a normalization factor for equalizing the energy level between the two signals, $${\mathrm{BOY\; WUT}}_{\mathit{HBN}}=\sqrt{\frac{{\displaystyle \underset{k=240}{\overset{319}{\Sigma }}}{U}_{\mathit{HB}1}{\left(\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">k</figure-callout>}\right)}^2+\epsilon }{{\displaystyle \underset{k=240}{\overset{319}{\Sigma }}}{\mathrm{<figure-callout\; id="2"\; label="U\; HBN\; k"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">U\; </figure-callout>}}_{\mathit{HBN}}{\left(k\right)}^{}{\left(\right)}^2+\epsilon }}$$

with ε = 0.01, and the coefficient α (between 0 and 1) is adjusted according to parameters estimated from the decoded low band and the coefficient β (between 0 and 1) depends on α .

$$E_{N4-6}={\displaystyle \sum _{k\in \mathrm{N}\left(160,239\right)}}{U\prime }^2\left(k\right)$$

$$E_{N4-6}={\displaystyle \sum _{k\in \mathrm{N}\left(240,319\right)}}{U\prime }^2\left(k\right)$$

où $$U\prime \left(k\right)=\{\begin{array}{cc}\sqrt{\frac{{\displaystyle \sum _{k=160}^{239}}{U}^2\left(k\right)}{{\displaystyle \sum _{k=80}^{159}}{U}^2\left(k\right)}U\left(k\right)}& k=80,\dots ,159\\ U\left(k\right)& k=160,\dots ,239\\ \sqrt{\frac{{\displaystyle \sum _{k=160}^{239}}{U}^2\left(k\right)}{{\displaystyle \sum _{k=240}^{319}}{U_{\mathrm{HB}1}}^2\left(k\right)}}& k=240,\dots ,319\end{array}$$

et N(k ₁, k ₂) est l'ensemble des indices k pour lesquels le coefficient d'indice k est classifié comme étant associé à du bruit. Cet ensemble peut être par exemple obtenu en détectant les pics locaux dans U'(k) vérifiant |U'(k)| ≥ |U'(k - 1)| et |U'(k) ≥ |U'(k + 1)| et en considérant que ces raies ne sont pas associés à du bruit, soit (en appliquant la négation de la condition précédente): $$\mathrm{N}\left(\mathrm{a},\mathrm{b}\right)=\left\{a\le k\le b|\left|U\prime \left(k\right)\right|<\left|U\prime \left(k-1\right)\right|\mathit{ou}\left|U\prime \left(k\right)\right|<\left|U\prime \left(k+1\right)\right|\right\}$$

On peut noter que d'autres méthodes de calcul de l'énergie du bruit sont possibles, par exemple en prenant la valeur médiane du spectre sur la bande considérée ou en appliquant un lissage à chaque raie fréquentielle avant de calculer l'énergie par bande.
On fixe α de telle sorte que le ratio entre l'énergie du bruit dans les bandes 4-6 kHz et 6-8 kHz soit le même qu'entre les bandes 2-4 kHz et 4-6 kHz : $$\alpha =\sqrt{\frac{\rho -E_{N6-8}}{{\displaystyle \sum _{k=160}^{239}}{U}^2\left(k\right)-E_{N6-8}}}$$

où $$E_{N4-6}=\max \left(E_{N4-6},E_{N2-4}\right),\mathit{\rho }=\frac{E_{N4-6}^2}{E_{N2-4}},\rho =\max \left(\rho ,E_{N6-8}\right)$$

Dans des variantes de l'invention, le calcul de α pourra être remplacé par d'autres méthodes. Par exemple, dans une variante, on pourra extraire (calculer) différents paramètres (ou « features » en anglais) caractérisant le signal en bande basse, dont un paramètre « tilt » similaire à celui calculé dans le codec AMR-WB, et on estimera le facteur α en fonction d'une régression linéaire à partir de ces différents paramètres en limitant sa valeur entre 0 et 1. La régression linéaire pourra par exemple être estimée de façon supervisée en estimant le facteur α en se donnant la bande haute originale dans une base d'apprentissage. On notera que le mode de calcul de α ne limite pas la nature de l'invention.
Dans un mode de réalisation privilégié, on prend $$\beta =\sqrt{1-{\alpha }^2}$$

afin de préserver l'énergie du signal étendu après mixage.
Dans une variante les facteurs β et α pourront être adaptés pour tenir compte du fait qu'un bruit injecté dans une bande donnée du signal est perçu en général comme plus fort qu'un signal harmonique à la même énergie dans la même bande. Ainsi on pourra modifier les facteurs β et α comme suit: $$\beta \leftarrow \beta \mathrm{.}f\left(\alpha \right)$$

$$\alpha \leftarrow \alpha \mathrm{.}f\left(\alpha \right)$$

où f(α) est une fonction décroissante de α, par exemple $f\left(\alpha \right)=b-a\sqrt{\alpha },$

b = 1.1, a = 1.2, f(α) limité de 0.3 à 1. Il faut remarquer qu'après multiplication par f(α), α ² + β ² < 1 si bien que l'énergie du signal U_HB2 (k) = βU _HB1 (k) + αG_HBNU_HBN(k) est plus basse que l'énergie de U _HB1(k) (la différence d'énergie dépend de α, plus on rajoute de bruit, plus l'énergie est atténuée).
Dans d'autres variantes de l'invention on pourra prendre : $$\beta =1-\alpha$$

ce qui permet de préserver le niveau d'amplitude (quand les signaux combinés sont de même signe) ; cependant cette variante a le désavantage de résulter en une énergie globale (au niveau de U_HB2 (k)) qui n'est pas monotone en fonction de α.
On remarque donc ici que le bloc 703 réalise l'équivalent du bloc 101 de la figure 1 pour normaliser le bruit blanc en fonction d'une excitation qui est par contre ici dans le domaine fréquentiel, déjà étendue à la cadence de 16 kHz ; de plus, le mixage est limité à la bande 6000-8000 Hz.In a preferred embodiment, the energy of the noise is calculated in three bands: 2000-4000 Hz, 4000-6000 Hz and 6000-8000 Hz, with $$E_{\mathrm{NOT}2-4}={\displaystyle \underset{k\in \mathrm{NOT}\left(80,159\right)}{\Sigma }}{U\text{'}}^2\left(k\right)$$

$$E_{\mathrm{NOT}4-6}={\displaystyle \underset{k\in \mathrm{NOT}\left(160,239\right)}{\Sigma }}{U\text{'}}^2\left(k\right)$$

$$E_{\mathrm{NOT}4-6}={\displaystyle \underset{k\in \mathrm{NOT}\left(240,319\right)}{\Sigma }}{U\text{'}}^2\left(k\right)$$

or $$U\text{'}\left(k\right)=\{\begin{array}{cc}\sqrt{\frac{{\displaystyle \underset{k=160}{\overset{239}{\Sigma }}}{U}^2\left(k\right)}{{\displaystyle \underset{k=80}{\overset{159}{\Sigma }}}{U}^2\left(k\right)}U\left(k\right)}& k=80,...,159\\ U\left(k\right)& k=160,...,239\\ \sqrt{\frac{{\displaystyle \underset{k=160}{\overset{239}{\Sigma }}}{U}^2\left(k\right)}{{\displaystyle \underset{k=240}{\overset{319}{\Sigma }}}{{\mathrm{<figure-callout\; id="1"\; label="U\; HB"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">U\; </figure-callout>}}_{\mathrm{HB}}}^2\left(k\right)}}& k=240,...,319\end{array}$$

and N ( k ₁ , k ₂ ) is the set of indices k for which the index coefficient k is classified as being associated with noise. This set can be obtained for example by detecting the local peaks in U '( k ) verifying | U '( k ) | ≥ | U '( k - 1) | and | U '( k ) ≥ | U '( k + 1) | and considering that these lines are not associated with noise, ie (by applying the negation of the previous condition): $$\mathrm{NOT}\left(\mathrm{at},\mathrm{b}\right)=\left\{\mathrm{at}\le k\le b|\left|U\text{'}\left(k\right)\right|<\left|U\text{'}\left(k-1\right)\right|\mathit{or}\left|U\text{'}\left(k\right)\right|<\left|U\text{'}\left(k+1\right)\right|\right\}$$

It may be noted that other methods of calculating the noise energy are possible, for example by taking the median value of the spectrum on the band in question or by applying a smoothing to each frequency line before calculating the energy per band.
We set α so that the ratio between the noise energy in the 4-6 kHz and 6-8 kHz bands is the same as between the 2-4 kHz and 4-6 kHz bands: $$\alpha =\sqrt{\frac{\rho -E_{\mathrm{NOT}6-8}}{{\displaystyle \underset{k=160}{\overset{239}{\Sigma }}}{U}^2\left(k\right)-E_{\mathrm{NOT}6-8}}}$$

or $$E_{\mathrm{NOT}4-6}=\max \left(E_{\mathrm{NOT}4-6},E_{\mathrm{NOT}2-4}\right),\mathit{\rho }=\frac{E_{\mathrm{NOT}4-6}^2}{E_{\mathrm{NOT}2-4}},\rho =\max \left(\rho ,E_{\mathrm{NOT}6-8}\right)$$

In variants of the invention, the calculation of α may be replaced by other methods. For example, in a variant, we can extract (calculate) different parameters (or "features") characterizing the low band signal, including a tilt parameter similar to that calculated in the AMR-WB codec, and estimating the α factor based on a linear regression from these parameters. different parameters by limiting its value between 0 and 1. The linear regression can for example be estimated in a supervised manner by estimating the factor α by giving the original high band in a learning base. Note that the calculation mode of α does not limit the nature of the invention.
In a preferred embodiment, we take $$\beta =\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="\alpha "\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}^2}$$

to preserve the energy of the extended signal after mixing.
In a variant, the factors β and α may be adapted to take account of the fact that noise injected into a given band of the signal is generally perceived as stronger than a harmonic signal at the same energy in the same band. Thus we can modify the factors β and α as follows: $$\beta \leftarrow \beta \mathrm{.}f\left(\alpha \right)$$

$$\alpha \leftarrow \alpha \mathrm{.}f\left(\alpha \right)$$

where f ( α ) is a decreasing function of α, for example $f\left(\alpha \right)=b-\mathrm{at}\sqrt{\alpha },$

b = 1.1, a = 1.2, f ( α ) limited from 0.3 to 1. It should be noted that after multiplication by f ( α ), α ² + β ² <1 so that the energy of the signal U _HB2 ( k ) = βU _{HB 1} (k) + αG _HBN U _HBN (k) is lower than the energy of U _{HB 1} ( k ) (the energy difference depends on α , the more noise is added, the more the energy is attenuated).
In other variants of the invention, it will be possible to take: $$\beta =1-\alpha$$

which preserves the amplitude level (when the combined signals are of the same sign); however, this variant has the disadvantage of resulting in a global energy (at U _HB2 ( k )) which is not monotonic as a function of α .
We note here that block 703 realizes the equivalent of block 101 of the figure 1 to normalize the white noise according to an excitation which is on the other hand here in the frequency domain, already extended to the rate of 16 kHz; in addition, the mix is limited to the band 6000-8000 Hz.

In a simple variant, an embodiment of block 703 may be considered, where the spectra, U _{HB 1} ( k ) or G _HBN U _HBN ( k ), are selected (switched) adaptively, which amounts to allowing only the values 0 or 1 for α ; this approach amounts to classifying the type of excitation to be generated in the 6000-8000 Hz band

The block 704 optionally carries out a dual operation of application of bandpass filter frequency response and deemphasis filtering (or deemphasis) in the frequency domain.

où G_deemph (k) est la réponse en fréquence du filtre 1/(1 - 0.68z ^-1) sur une bande de fréquence discrète restreinte. En prenant en compte les fréquences discrètes (impaires) de la DCT-IV, on définit ici G_deemph (k) comme: $$G_{\mathit{deemph}}\left(k\right)=\frac{1}{\left|e^{{\mathit{j\theta }}_k}-0.68\right|},k=0,\cdots ,255$$

où $${\theta }_k=\frac{256-80+k+\frac{1}{2}}{256}\mathrm{.}$$

Dans le cas où une autre transformation que la DCT-IV est utilisée, la définition de θ_k pourra être ajustée (par exemple pour des fréquences paires).
On note que la désaccentuation est appliquée en deux phases pour k = 200,...,255 correspondant à la bande de fréquence 5000-6400 Hz, où la réponse 1/(1-0.68z ^-1) est appliquée comme à 12.8 kHz, et pour k = 256,...,319 correspondant à la bande de fréquence 6400-8000 Hz, où la réponse est étendue de 16 kHz ici à une valeur constante dans la bande 6.4-8 kHz.In a variant of the invention, the deemphasis filtering may be performed in the time domain, after block 705 or even before block 700; however, in this case, bandpass filtering performed in block 704 may leave some low frequency components of very low levels that are amplified by de-emphasis, which may slightly discern the decoded low band. For this reason, it is preferred here to perform the deemphasis in the frequency domain. In the preferred embodiment, the index coefficients k = 0,..., 199 are set to zero, so the deemphasis is limited to the higher coefficients.
The excitation is first de-emphasized according to the following equation: $$U_{\mathit{HB}2}\text{'}\left(k\right)=\{\begin{array}{cc}0\hfill & k=0,\cdots ,199\hfill \\ {\mathrm{BOY\; WUT}}_{\mathit{deempth}}\left(k\right)U_{\mathit{HB}2}\left(k\right)\hfill & k=200,\cdots ,255\hfill \\ {\mathrm{BOY\; WUT}}_{\mathit{deemph}}\left(255\right)U_{\mathit{HB}2}\left(k\right)\hfill & k=256,\cdots ,319\hfill \end{array}$$

where G _deemph ( k ) is the frequency response of the filter 1 / (1 - 0.68 z ^-1 ) over a restricted discrete frequency band. Taking into account the discrete (odd) frequencies of the DCT-IV, we define here G _deemph ( k ) as: $${\mathrm{BOY\; WUT}}_{\mathit{deemph}}\left(k\right)=\frac{1}{\left|e^{{\mathit{j\theta }}_k}-0.68\right|},k=0,\cdots ,255$$

or $${\theta }_k=\frac{256-80+k+\frac{1}{2}}{256}\mathrm{.}$$

In the case where another transformation than the DCT-IV is used, the definition of θ _k can be adjusted (for example for even frequencies).
It is noted that the deemphasis is applied in two phases for k = 200, ..., 255 corresponding to the frequency band 5000-6400 Hz, where the response 1 / (1-0.68 z ^-1 ) is applied as at 12.8 kHz , and for k = 256, ..., 319 corresponding to the 6400-8000 Hz frequency band, where the response is extended from 16 kHz here to a constant value in the 6.4-8 kHz band.

It may be noted that in the AMR-WB codec the HF synthesis is not de-emphasized. In the embodiment presented here, the high frequency signal is on the contrary de-emphasized so as to bring it back into a domain consistent with the low signal. frequencies (0-6.4 kHz) coming out of block 305 of the figure 3 . This is important for the estimation and subsequent adjustment of the energy of the HF synthesis.

In a variant of the embodiment, in order to reduce the complexity, it is possible to fix G _deemph ( k ) to a constant value independent of k , taking for example G _deemph ( k ) = 0.6 which corresponds approximately to the average value of G _deemph ( k ) for k = 200, ..., 319 under the conditions of the embodiment described above.

In another variant of the embodiment of the extension device, the de-emphasis can be performed in an equivalent way in the time domain after inverse DCT.

In addition to de-emphasis, band-pass filtering is applied with two separate parts: one fixed high-pass, the other adaptive low-pass (flow-rate function).

This filtering is performed in the frequency domain.

où N_lp =60 à 6.6 kbit/s, 40 à 8.85 kbit/s, 20 aux débits >8.85 bit/s. Ensuite on applique un filtre passe-bande sous la forme : $$U_{\mathit{HB}3}\left(k\right)=\{\begin{array}{cc}0\hfill & k=0,\cdots ,199\hfill \\ G_{\mathit{hp}}\left(k-200\right)U_{\mathit{HB}2}\prime \left(k\right)\hfill & k=200,\cdots ,255\hfill \\ U_{\mathit{HB}2}\prime \left(k\right)\hfill & k=256,\cdots ,319-N_{\mathrm{lp}}\hfill \\ G_{\mathit{lp}}\left(k-320-N_{\mathrm{lp}}\right)U_{\mathit{HB}2}\prime \left(k\right)\hfill & k=320-N_{\mathrm{lp}},\cdots ,319\hfill \end{array}$$

La définition de G_hp (k), k = 0,...,55, est donnée par exemple au tableau 2 ci-dessous. Tableau 2 K g_hp (k) K g_hp (k) K g_hp (k) k g_hp (k) 0 0.001622428 14 0.114057967 28 0.403990611 42 0.776551214 1 0.004717458 15 0.128865425 29 0.430149896 43 0.800503267 2 0.008410494 16 0.144662643 30 0.456722014 44 0.823611104 3 0.012747280 17 0.161445005 31 0.483628433 45 0.845788355 4 0.017772424 18 0.179202219 32 0.510787115 46 0.866951597 5 0.023528982 19 0.197918220 33 0.538112915 47 0.887020781 6 0.030058032 20 0.217571104 34 0.565518011 48 0.905919644 7 0.037398264 21 0.238133114 35 0.592912340 49 0.923576092 8 0.045585564 22 0.259570657 36 0.620204057 50 0.939922577 9 0.054652620 23 0.281844373 37 0.647300005 51 0.954896429 10 0.064628539 24 0.304909235 38 0.674106188 52 0.968440179 11 0.075538482 25 0.328714699 39 0.700528260 53 0.980501849 12 0.087403328 26 0.353204886 40 0.726472003 54 0.991035206 13 0.100239356 27 0.378318805 41 0.751843820 55 1.000000000 On notera que dans des variantes de l'invention les valeurs de G_hp (k) pourront être modifiées tout en gardant une atténuation progressive. De même le filtrage passe-bas à largeur de bande variable, G_lp (k), pourra être ajusté avec des valeurs ou un support fréquentiel différents, sans changer le principe de cette étape de filtrage.In the preferred embodiment, the partial low-pass filter response in the frequency domain is calculated as follows: $${\mathrm{BOY\; WUT}}_{\mathit{lp}}\left(k\right)=1-0999\frac{k}{{\mathrm{NOT}}_{\mathit{lp}}-1}$$

where N _lp = 60 to 6.6 kbit / s, 40 to 8.85 kbit / s, 20 at rates> 8.85 bit / s. Then we apply a bandpass filter in the form: $$U_{\mathit{HB}3}\left(k\right)=\{\begin{array}{cc}0\hfill & k=0,\cdots ,199\hfill \\ {\mathrm{BOY\; WUT}}_{\mathit{hp}}\left(k-200\right)U_{\mathit{HB}2}\text{'}\left(k\right)\hfill & k=200,\cdots ,255\hfill \\ U_{\mathit{HB}2}\text{'}\left(k\right)\hfill & k=256,\cdots ,319-{\mathrm{NOT}}_{\mathrm{lp}}\hfill \\ {\mathrm{BOY\; WUT}}_{\mathit{lp}}\left(k-320-{\mathrm{NOT}}_{\mathrm{lp}}\right)U_{\mathit{HB}2}\text{'}\left(k\right)\hfill & k=320-{\mathrm{NOT}}_{\mathrm{lp}},\cdots ,319\hfill \end{array}$$

The definition of G _hp ( k ), k = 0, ..., 55, is given for example in Table 2 below. <b> Table 2 </ b> K g _hp ( k ) K g _hp ( k ) K g _hp ( k ) k g _hp ( k ) 0 0.001622428 14 0.114057967 28 0.403990611 42 0.776551214 1 0.004717458 15 0.128865425 29 0.430149896 43 0.800503267 2 0.008410494 16 0.144662643 30 0.456722014 44 0.823611104 3 0.012747280 17 0.161445005 31 0.483628433 45 0.845788355 4 0.017772424 18 0.179202219 32 0.510787115 46 0.866951597 5 0.023528982 19 0.197918220 33 0.538112915 47 0.887020781 6 0.030058032 20 0.217571104 34 0.565518011 48 0.905919644 7 0.037398264 21 0.238133114 35 0.592912340 49 0.923576092 8 0.045585564 22 0.259570657 36 0.620204057 50 0.939922577 9 0.054652620 23 0.281844373 37 0.647300005 51 0.954896429 10 0.064628539 24 0.304909235 38 0.674106188 52 0.968440179 11 0.075538482 25 0.328714699 39 0.700528260 53 0.980501849 12 0.087403328 26 0.353204886 40 0.726472003 54 0.991035206 13 0.100239356 27 0.378318805 41 0.751843820 55 1.000000000 It will be noted that in variants of the invention the values of G _hp ( k ) may be modified while keeping a gradual attenuation. Similarly, the variable bandwidth low-pass filtering, G _lp ( k ), may be adjusted with different values or frequency support, without changing the principle of this filtering step.

Note also that the bandpass filtering can be adapted by defining a single filtering step combining the high-pass and low-pass filtering.

In another embodiment, the bandpass filtering may be performed in an equivalent manner in the time domain (as in block 112 of the present invention). figure 1 ) with different filter coefficients according to the flow rate, after a reverse DCT step. However, it will be noted that it is advantageous to carry out this step directly in the frequency domain because the filtering is carried out in the field of LPC excitation and therefore the problems of circular convolution and edge effects are very limited in this field. .

It will also be noted that in the case of the 23.85 kbit / s rate, the deemphasis of the excitation U _HB2 ( k ) is not carried out in order to remain in agreement with the way in which the correction gain is calculated in the AMR-WB encoder. and to avoid double multiplications. In this case block 704 only performs the low-pass filtering.

où N _16k = 320 et k = 0, ..., 319. Cette excitation échantillonnée à 16 kHz est ensuite de façon optionnelle mise à l'échelle par des gains définis par sous-trame de 80 échantillons (bloc 707).
Dans un mode de réalisation privilégié, on calcule d'abord (bloc 706) un gain g_HB1(m) par sous-trame par des ratios d'énergie des sous-trames tel que dans chaque sous-trame d'indice m=0, 1, 2 ou 3 de la trame courante: $$g_{\mathit{HB}1}\left(m\right)=\sqrt{\frac{e_3\left(m\right)}{e_2\left(m\right)}}$$

où $$e_1\left(m\right)={\displaystyle \sum _{n=0}^{63}}u{\left(n+64m\right)}^2+\epsilon$$

$$e_2\left(m\right)={\displaystyle \sum _{n=0}^{79}}{u}_{\mathit{HB}0}{\left(n+80m\right)}^2+\epsilon$$

$$e_3\left(m\right)=e_1\left(m\right)\frac{{\displaystyle \sum _{n=0}^{319}}{u}_{\mathit{HB}0}{\left(n\right)}^2+\epsilon }{{\displaystyle \sum _{n=0}^{255}}u{\left(n\right)}^2+\epsilon }$$

avec ε = 0.01. On peut écrire le gain par sous-trame g _HB1(m) sous la forme : $$g_{\mathit{HB}1}\left(m\right)=\sqrt{\frac{\frac{{\displaystyle \sum _{n=0}^{63}}u{\left(n+64m\right)}^2+\epsilon }{{\displaystyle \sum _{n=0}^{255}}u{\left(n\right)}^2+\epsilon }}{\frac{{\displaystyle \sum _{n=0}^{79}}{u}_{\mathit{HB}0}{\left(n+80m\right)}^2+\epsilon }{{\displaystyle \sum _{n=0}^{319}}{u}_{\mathit{HB}0}{\left(n\right)}^2+\epsilon }}}$$

ce qui montre qu'on assure dans le signal u_HB le même ratio entre énergie par sous-trame et énergie par trame que dans le signal u(n).
Le bloc 707 effectue la mise à l'échelle du signal combiné selon l'équation suivante: $$u_{\mathit{HB}}\left(n\right)=g_{\mathit{HB}1}\left(m\right)u_{\mathit{HB}0}\left(n\right),n=80m,\cdots ,80\left(m+1\right)-1$$

The inverse transform block 705 performs an inverse DCT on 320 samples to find the high-frequency excitation sampled at 16 kHz. Its implementation is identical to block 700, since the DCT-IV is orthonormed, except that the length of the transform is 320 instead of 256, and we obtain: $${\mathrm{<figure-callout\; id="0"\; label="u\; HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}\left(\mathrm{not}\right)={\displaystyle \underset{k=0}{\overset{{\mathrm{NOT}}_{16k}-1}{\Sigma }}}{U}_{\mathit{HB}3}\left(k\right)\cos \left(\frac{\pi }{{\mathrm{NOT}}_{16k}}\left(k+\frac{1}{2}\right)\left(\mathrm{not}+\frac{1}{2}\right)\right)$$

where N _{16 k} = 320 and k = 0, ..., 319 . This excitation sampled at 16 kHz is then optionally scaled by gains defined by subframe of 80 samples (block 707).
In a preferred embodiment, a gain g _HB1 (m) per sub-frame is first calculated (block 706) by sub-frame energy ratios such as in each sub-frame of index m = 0 , 1, 2 or 3 of the current frame: $${\mathrm{boy\; Wut}}_{\mathit{HB}1}\left(m\right)=\sqrt{\frac{e_3\left(m\right)}{e_2\left(m\right)}}$$

or $$e_1\left(m\right)={\displaystyle \underset{\mathrm{not}=0}{\overset{63}{\Sigma }}}u{\left(\mathrm{not}+64\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">m</figure-callout>}\right)}^2+\epsilon$$

$$e_2\left(m\right)={\displaystyle \underset{\mathrm{not}=0}{\overset{79}{\Sigma }}}{\mathrm{<figure-callout\; id="0"\; label="u\; HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}{\left(\mathrm{not}+80\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">m</figure-callout>}\right)}^2+\epsilon$$

$$e_3\left(m\right)=e_1\left(m\right)\frac{{\displaystyle \underset{\mathrm{not}=0}{\overset{319}{\Sigma }}}{\mathrm{<figure-callout\; id="0"\; label="u\; HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}{\left(\mathrm{not}\right)}^2+\epsilon }{{\displaystyle \underset{\mathrm{not}=0}{\overset{255}{\Sigma }}}u{\left(\mathrm{not}\right)}^2+\epsilon }$$

with ε = 0.01. We can write the gain by subframe g _{HB 1} ( m ) in the form: $${\mathrm{boy\; Wut}}_{\mathit{HB}1}\left(m\right)=\sqrt{\frac{\frac{{\displaystyle \underset{\mathrm{not}=0}{\overset{63}{\Sigma }}}u{\left(\mathrm{not}+64\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">m</figure-callout>}\right)}^2+\epsilon }{{\displaystyle \underset{\mathrm{not}=0}{\overset{255}{\Sigma }}}u{\left(\mathrm{not}\right)}^2+\epsilon }}{\frac{{\displaystyle \underset{\mathrm{not}=0}{\overset{79}{\Sigma }}}{\mathrm{<figure-callout\; id="0"\; label="u\; HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}{\left(\mathrm{not}+80\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">m</figure-callout>}\right)}^2+\epsilon }{{\displaystyle \underset{\mathrm{not}=0}{\overset{319}{\Sigma }}}{\mathrm{<figure-callout\; id="0"\; label="u\; HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}{\left(\mathrm{not}\right)}^2+\epsilon }}}$$

which shows that the signal u _{HB has} the same ratio between energy per subframe and energy per frame as in the signal u ( n ).
Block 707 scales the combined signal according to the following equation: $$u_{\mathit{HB}}\left(\mathrm{not}\right)={\mathrm{boy\; Wut}}_{\mathit{HB}1}\left(m\right){\mathrm{<figure-callout\; id="0"\; label="u\; HB"\; filenames="imgf0002.png,imgf0005.png"\; state="\{\{state\}\}">u\; </figure-callout>}}_{\mathit{HB}}\left(\mathrm{not}\right),\mathrm{not}=80m,\cdots ,80\left(m+1\right)-1$$

Note that the realization of the block 706 differs from that of the block 101 of the figure 1 because the energy at the current frame is taken into account in addition to that of the sub-frame. This makes it possible to have the ratio of the energy of each sub-frame with respect to the energy of the frame. Energy ratios (or relative energies) are compared rather than the absolute energies between low band and high band.

Thus, this scaling step makes it possible to keep in the high band the energy ratio between the subframe and the frame in the same way as in the low band.

It will be noted here that in the case of the 23.85 kbit / s rate the gains g _{HB 1} ( m ) are calculated but applied in the next step, as explained with reference to FIG. figure 4 , to avoid double multiplications. In this case u _HB ( n ) = u _{HB 0} ( n ).

According to the invention, the block 708 then performs a scaling factor calculation by subframe of the signal (steps E602 to E 603 of the figure 6 ), as previously described with reference to the figure 6 and detailed in figure 4 and 5 .

Finally, the corrected excitation u _HB '( n ) is filtered by the filtering module 710 which can be achieved here by taking the transfer function 1 / Å (z / γ ), where γ = 0.9 to 6.6 kbit / s and γ = 0.6 at other flow rates, which limits the order of the filter to order 16.
In a variant, this filtering can be done in the same way as that described for block 111 of the figure 1 of the AMR-WB decoder, however the order of the filter goes to 20 at the rate of 6.6, which does not significantly change the quality of the synthesized signal. In another variant, it will be possible to carry out LPC synthesis filtering in the frequency domain, after having calculated the frequency response of the filter implemented in block 710.

In an alternative embodiment, the step of filtering by a linear prediction filter 710 for the second frequency band is combined with the application of the optimized scaling factor, which reduces the processing complexity. Thus, the filtering steps 1 / Å (z / γ ) and the application of the optimized scaling factor g _{HB 2} are combined with a single filtering step g _{HB 2} / Å (z / γ ) to reduce the processing complexity. .

In alternative embodiments of the invention, the coding of the low band (0-6.4 kHz) may be replaced by a CELP coder other than that used in AMR-WB, for example the CELP coder in G.718 to 8. kbit / s. Without loss of generality other encoders in wide band or operating at frequencies higher than 16 kHz, in which the coding of the low band operates at an internal frequency at 12.8 kHz could be used. Moreover, the invention can be obviously adapted to other sampling frequencies than 12.8 kHz, when a low frequency encoder operates at a sampling frequency lower than that of the original or reconstructed signal. When the low band decoding does not use a linear prediction, it does not have an excitation signal to be extended, in this case it will be possible to carry out an LPC analysis of the reconstructed signal in the current frame and calculate an LPC excitation. so as to be able to apply the invention.

Finally, in another variant of the invention, the excitation ( u ( n )) is resampled, for example by linear interpolation or "spline" cubic, from 12.8 to 16 kHz before transformation (for example DCT-IV) This variant has the defect of being more complex, because the transform (DCT-IV) of the excitation is then calculated over a greater length and the resampling is not carried out in the field of the transformed.

Moreover, in variants of the invention, all the calculations necessary for the estimation of the gains ( _GHBN , g _{HB 1} ( m ), g _{HB 2} ( m ), g _HBN , ...) can be carried out in a logarithmic domain.

In variants of the band extension, the low band excitation u ( n ) and the LPC 1 / Â (z) filter will be estimated per frame, by LPC analysis of a low band signal whose band must be extended. The low band excitation signal is then extracted by analyzing the audio signal.

In a possible embodiment of this variant, the low band audio signal is resampled before the excitation extraction step, so that the excitation extracted from the audio signal (by linear prediction) is already resolved. sampled.

The illustrated tape extension at figure 7 , applies in this case to a low band which is not decoded but analyzed.

The figure 8 represents an embodiment of a device for determining an optimized scale factor 800 according to the invention. This may be an integral part of an audio-frequency signal decoder or equipment receiving decoded or non-decoded audio signals.

This type of device comprises a PROC processor cooperating with a memory block BM having a memory storage and / or work MEM.
Such a device comprises an input module E adapted to receive a decoded or extracted excitation audio signal in a first so-called low band frequency band ( u ( n ) or U ( k ))
and the parameters of a linear prediction synthesis filter ( λ ( z )). It comprises an output module S adapted to transmit the synthesized and optimized high frequency signal (u _HB '(n)) for example to a filtering module such as block 710 of FIG. figure 7 or a resampling module like module 311 of the figure 3 .

The memory block may advantageously comprise a computer program comprising code instructions for carrying out the steps of the method for determining an optimized scale factor to be applied to an excitation signal or to a filter within the meaning of FIG. invention, when these instructions are executed by the processor PROC, and in particular the steps of determination (E602) of a linear prediction filter called additional filter, of order less than the linear prediction filter of the first frequency band, the coefficients additional filter being obtained from the parameters decoded or extracted from the first frequency band, calculation (E603) of an optimized scale factor according to at least the coefficients of the additional filter.

Typically, the description of the figure 6 takes the steps of an algorithm of such a computer program. The computer program can also be stored on a memory medium readable by a reader of the device or downloadable in the memory space thereof.

The memory MEM generally records all the data necessary for the implementation of the method.

In one possible embodiment, the device thus described may also include the functions of applying the optimized scaling factor to the extended excitation signal, frequency band extension, low band decoding and other processing functions. described for example in figure 3 and 4 in addition to the optimized scale factor determination functions according to the invention.

Claims (11)

1. Method for determining an optimized scale factor to be applied to an excitation signal or to a filter in an audio frequency signal frequency band extension method, the band extension method (E601) comprising a step of decoding or of extraction, in a first frequency band, of an excitation signal and of parameters of the first frequency band comprising coefficients of a linear prediction filter, a step of generation of an extended excitation signal on at least one second frequency band and a step of filtering, by a linear prediction filter, for the second frequency band, the determination method being characterized in that it comprises the following steps:

   - determination (E602) of a linear prediction filter called additional filter, of lower order than the linear prediction filter of the first frequency band, the coefficients of the additional filter being obtained from the parameters decoded or extracted from the first frequency band; and

   - computation (E603) of the optimized scale factor as a function at least of the coefficients of the additional filter.
2. Method according to Claim 1, characterized in that the band extension method comprises a step of application (E604) of the optimized scale factor to the extended excitation signal.
3. Method according to Claim 2, characterized in that the application of the optimized scale factor is combined with the step of filtering in the second frequency band.
4. Method according to Claim 1, characterized in that the coefficients of the additional filter are obtained by truncation of the transfer function of the linear prediction filter of the first frequency band to obtain a lower order.
5. Method according to Claim 4, characterized in that the coefficients of the additional filter are modified as a function of a stability criterion of the additional filter.
6. Method according to Claim 1, characterized in that the computation of the optimized scale factor comprises the following steps:

   - computation of the frequency responses of the linear prediction filters of the first and second frequency bands for a common frequency;

   - computation of the frequency response of the additional filter for this common frequency;

   - computation of the optimized scale factor as a function of the duly computed frequency responses.
7. Method according to Claim 1, characterized in that it further comprises the following steps, implemented for a predetermined decoding bit rate:

   - first scaling of the extended excitation signal by a gain computed for each subframe as a function of an energy ratio between the decoded excitation signal and the extended excitation signal;

   - second scaling of the excitation signal obtained from the first scaling by a decoded correction gain;

   - adjustment of the energy of the excitation for the current subframe by an adjustment factor computed as a function of the energy of the signal obtained after the second scaling and as a function of the signal obtained after application of the optimized scale factor.
8. Device for determining an optimized scale factor to be applied to an excitation signal or to a filter in an audio frequency signal frequency band extension device, the band extension device (400) comprising a module for decoding or extracting, in a first frequency band, an excitation signal and parameters of the first frequency band comprising coefficients of a linear prediction filter, a module for generating an extended excitation signal on at least one second frequency band and a module for filtering, by a linear prediction filter, for the second frequency band, the determination device being characterized in that it comprises:

   - a module (401a) for determining a linear prediction filter called additional filter, of lower order than the linear prediction filter of the first frequency band, the coefficients of the additional filter being obtained from the parameters decoded or extracted from the first frequency band; and

   - a module (401b) for computing the optimized scale factor as a function at least of the coefficients of the additional filter.
9. Audio frequency signal decoder, characterized in that it comprises a device for determining an optimized scale factor according to Claim 8.
10. Computer program comprising code instructions for implementing the steps of the method for determining an optimized scale factor according to one of Claims 1 to 7, when these instructions are executed by a processor.
11. Storage medium that can be read by a device for determining an optimized scale factor on which is stored a computer program comprising code instructions for the execution of steps of the method for determining an optimized scale factor according to one of Claims 1 to 7.

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