EP1438871B1 - Device for capturing and restoring sound using several sensors - Google Patents

Abstract

The invention concerns a system for processing a sound signal comprising an amplifier, an analog-to-digital conversion circuit or a digital-to-analog conversion circuit, a filtering circuit, end processing elements and a circuit for adding filtered signals, so as to deliver at least an output signal, said end processing elements being sound sensors or loudspeakers. The invention is characterized in that the filtering circuit is optimized in accordance with the characteristics particular to the end processing elements and in accordance with their geometric implantation and it comprises at least a directive lobe and an output circuit delivering an output signal through directive lobe.

Description

• La prise de sons en audiovisuel. Le système permet de remplacer un ou plusieurs microphones, en garantissant une grande qualité du son capté, et en permettant des diagrammes de directivités arbitraires (contrairement aux diagrammes de directivité des microphones analogiques qui sont obtenus par des moyens purement acoustiques et subissent donc les lois de la propagation des sons).
• Le terminal d'audioconférence. Le système permet d'assurer la capture du son (microphones) et la restitution du son (haut-parleurs) tout en minimisant l'écho induit depuis le haut-parleur vers le microphone.
• Les installation de « public adress ». La directivité du système permet de réduire fortement l'effet Larsen, et donc d'améliorer le niveau d'émission du signal sonore.
• Les équipements de reconnaissance de parole, dans des contextes de bureautique, de voiture, de bornes interactives...

The present invention relates to the field of sound recording and sound reproduction. It relates in particular to a system that can be used as a sound sensor only, or simultaneously in capturing and restoring the sound. The targeted applications are:

• Sound recording in audiovisual. The system makes it possible to replace one or more microphones, by guaranteeing a high quality of the sound picked up, and by allowing arbitrary directivity diagrams (contrary to the directivity diagrams of the analog microphones which are obtained by purely acoustic means and thus undergo the laws of the propagation of sounds).
• The audio conference terminal. The system allows sound capture (microphones) and sound reproduction (speakers) while minimizing the echo induced from the speaker to the microphone.
• The installation of "public addresses". The directivity of the system can greatly reduce the feedback effect, and thus improve the level of emission of the sound signal.
• Speech recognition equipment, in office, car, interactive kiosk contexts ...

The problem posed by the devices of the prior art stems from the inhomogeneity of the spatial curve of sensitivity, as well as difficulty in adapting the sensitivity curve to the displacements of the sound source.

It has been proposed in the prior art a solution described in the French patent FR2728753 describing a sound pickup device associated with a pointing system to improve the acquisition conditions of the sensors.

This solution is expensive and difficult to implement.

The document WO 97/46048 teaches a system according to the preamble of claim 1. However, this system does not allow a good adaptation to the displacements of the sound source. The invention aims to remedy the aforementioned problems by an effective solution that does not require a pointing solution.

For this purpose, the invention relates to a system according to claim 1.

According to a variant, the processing system is a system for acquiring a sound signal and in that the end processing elements are sound sensors.

Advantageously, the sound sensors are distributed along a plurality of concentric axes.

Preferably, the sound sensors are distributed along a plurality of coplanar axes.

According to a particular mode of implementation, the sound sensors are distributed along three axes forming an angle of 120 ° between them.

According to another particular mode of implementation, the sound sensors are distributed along five axes oriented respectively with an angle of 0 °, ± 30 °, ± 110 ° with respect to a reference axis.

According to one variant, the output circuit delivers several output signals each corresponding to a directional lobe, these different output signals being recomposed to form a single signal corresponding to the sum of the directive signals weighted by the energy of the corresponding lobe.

où :
S(f) désigne l'amplitude du signal de sortie en fonction de la fréquence
L_n,θ(f) désigne un facteur de pondération fonction de l'identifiant du premier lobe, et de l'angle de la source,
L_n+1,θ(f) désigne un facteur de pondération fonction de l'identifiant du deuxième lobe, et de l'angle de la source,
S_n(f) désigne l'amplitude du signal du premier lobe
S_n+1(f) désigne l'amplitude du signal du deuxième lobe.Advantageously, the output circuit delivers several output signals each corresponding to a directional lobe, these different output signals being recomposed to form a single signal corresponding to: $$S\left(f\right)={\mathrm{The}}_{\mathrm{not},\theta }\left(f\right)S_{\mathrm{not}}\left(f\right)+{\mathrm{The}}_{\mathrm{not}+1,\theta }\left(f\right)S_{\mathrm{not}+1}\left(f\right)$$

or :
S (f) denotes the amplitude of the output signal as a function of frequency
L _{n, θ} (f) denotes a weighting factor according to the identifier of the first lobe, and the angle of the source,
L _{n + 1, θ} (f) denotes a weighting factor that is a function of the identifier of the second lobe, and the angle of the source,
S _n (f) denotes the amplitude of the signal of the first lobe
S _{n + 1} (f) denotes the signal amplitude of the second lobe.

According to a particular embodiment, the output circuit delivers several output signals each corresponding to a directional lobe, these different output signals being each interpreted in a differentiated manner without recomposition.

According to a variant, the processing system is a system for restoring a sound signal and in that the end processing elements are loudspeakers.

Preferably, the loudspeakers are distributed according to a plurality of concentric axes.

Advantageously, the loudspeakers are distributed along a plurality of coplanar axes.

According to a particular mode of implementation, the loudspeakers are distributed along three axes forming an angle of 120 ° between them.

According to another particular mode of implementation, the loudspeakers are distributed along five axes oriented respectively with an angle of 0 °, ± 30 °, ± 110 ° with respect to a reference axis.

Advantageously, the output circuit broadcasts several output signals each corresponding to a directional lobe, each output signal being diffused in its directional lobe.

According to one variant, the processing system is a sound acquisition and reproduction system, in that the end processing elements are loudspeakers or sound sensors and in that it comprises filtering filters. acquisition and restitution filters.

Advantageously, the acquisition filters are optimized not to receive the signal emitted by the speakers and in that the playback filters are optimized not to send a signal on the sound sensors.

Preferably, the geometry of the loudspeakers is positioned on an axis perpendicular to the plane of the sound sensors.

Advantageously, the sound sensors are placed on hyperbolas located in vertical planes.

• la figure 1 représente une vue schématique du placement logarithmique des capteurs sur une droite ;
• la figure 2 représente une vue schématique du placement des capteurs sur un ensemble de droites issues d'une origine commune ;
• la figure 3 représente une vue schématique du placement des haut-parleurs relativement aux microphones
• la figure 4 représente une vue schématique du placement des capteurs sur une hyperbole ;
• la figure 5 représente une vue schématique d'une structure du dispositif d'acquisition avec une seule voie de sortie ;
• la figure 6 représente une vue schématique d'une structure du dispositif d'acquisition avec plusieurs voies de sortie ;
• la figure 7 représente une vue schématique d'une structure du dispositif de sélection des voies par l'énergie ;
• la figure 8 représente une vue schématique d'une structure du dispositif de sélection des voies par la position ;
• la figure 9 représente une vue schématique d'une structure du dispositif de restitution ;
• la figure 10 représente une vue schématique d'une structure du dispositif complet avec acquisition sur une voie et restitution ;
• la figure 11 représente une vue schématique d'une structure du dispositif complet avec acquisition sur plusieurs voies et restitution ;
• la figure 12 représente une vue schématique des hypothèses sur le bruit propre des capteurs ;
• la figure 13 représente une vue schématique du dispositif de restitution avec plusieurs voies de sortie, chacune étant diffusée dans un lobe directif.

The invention will be better understood on reading the description which follows, relating to a non-limiting embodiment of the invention, with reference to the appended drawings in which:

• the figure 1 represents a schematic view of the logarithmic placement of the sensors on a line;
• the figure 2 represents a schematic view of the placement of the sensors on a set of lines originating from a common origin;
• the figure 3 represents a schematic view of speaker placement relative to microphones
• the figure 4 represents a schematic view of the placement of the sensors on a hyperbola;
• the figure 5 is a schematic view of a structure of the acquisition device with a single output channel;
• the figure 6 represents a schematic view of a structure of the acquisition device with several output channels;
• the figure 7 represents a schematic view of a structure of the channel selection device by the energy;
• the figure 8 is a schematic view of a structure of the track selection device by the position;
• the figure 9 represents a schematic view of a structure of the rendering device;
• the figure 10 represents a schematic view of a structure of the complete device with acquisition on a track and restitution;
• the figure 11 represents a schematic view of a structure of the complete device with multi-channel acquisition and rendering;
• the figure 12 represents a schematic view of the assumptions about the noise of the sensors;
• the figure 13 represents a schematic view of the rendering device with several output channels, each being diffused in a directional lobe.

• une partie destinée à la prise de sons,
• une partie destinée à la restitution des sons,
• une partie assurant le couplage entre les deux parties ci-dessus.

The invention relates to a system for sound recording, or for sound recording and sound reproduction. It uses a plurality of sensors, including microphones, forming a network with one, two or three dimensions. This system is digital and consists of:

• a part intended for taking sounds,
• a part intended for the restitution of the sounds,
• a part ensuring the coupling between the two parts above.

The invention lies in particular in the placement of these sensors in space, to form a network with well defined geometric characteristics.

The part making the taking of sounds is represented in figure 6 schematically. It consists of a set of M sensors (1, 11, 21, 31). These sensors are constituted by microphonic cells, for example electrets providing an analog electrical signal from the sound captured. Each sensor is connected to an optional pre-amplification stage (2, 12, 22, 32), also providing, if necessary, high-pass filtering in order to attenuate the components whose frequencies are between 0 Hz and the cut-off frequency of this high-pass filter, this cut-off frequency being generally between 20 Hz and 200 Hz.

Each preamplifier is connected to an analog-digital converter (3, 13, 23, 33), responsible for transforming the analog electrical signal into a sequence of samples, at a rate of F _e per second, each represented by an encoded value on B bits (typically B = ₂₄ bits, but other values could be used, such as B = 16 bits, B = 18 bits, B = ₂₀ bits),

These analog-to-digital converters are connected to a digital delay line type circuit (4, 14, 24, 34) making it possible to delay each signal by a fixed number of sampling periods, the number being a priori different for each signal.

Each digital delay line is connected to a circuit (5, 15, 25, 35) for distributing these signals to one or more signal processing microprocessors (DSPs for "Digital Signal Processor"),

Each DSP is connected to a circuit for transmitting the digital signal from the DSP to for example a recorder or a mixing console (this circuit could for example be a transmitter in the AES-3 format) or to a digital telecommunications network ( ISDN type, or TCP / IP type).

• filtrer par un filtre numérique, chaque signal issu d'un capteur,
• additionner l'ensemble des ^M signaux filtrés,
• normaliser l'amplitude du signal résultant, en le multipliant par un coefficient fixe,
• éventuellement filtrer le signal résultant par un filtre numérique.

The treatment performed by the DSP (s) consists of:

• filter by a digital filter, each signal coming from a sensor,
• add up all the ^M filtered signals,
• standardize the amplitude of the resulting signal, multiplying it by a fixed coefficient,
• possibly filter the resulting signal by a digital filter.

The structure of the treatment conforms, for example, to the article of S.Haykin and T.Kesler, "Relation between the radiation pattern of an array and the two-dimensional discrete Fourier transform" published in the journal IEEE Transactions on Antennas and Propagation, Volume 23, Number 3, pages 419-420, 1975 .

The part ensuring the restitution of sounds is represented by the figure 9 . It consists of a signal processing processor (DSP) receiving the digital signal to be reproduced, and manufacturer using P filters digital (100, 110, 120, 130), P filtered versions of this signal to be rendered.

Behind each of the digital filters, a digital delay line type circuit (101, 111, 121, 131) makes it possible to delay each signal by a fixed number of sampling periods, the number being a priori different for each signal.

Each-digital delay line is connected to a digital to analog converter (102, 112, 122, 132) responsible for transforming the sequence of samples at a rate of F _e per second, into an analog electrical signal,

The converters are connected to an optional amplification stage (103, 113, 123, 133).

Each of the amplifiers is connected to a loudspeaker providing sound from the analog electrical signal.

The part ensuring the restitution of the sounds is presented in figure 13 in a variant that allows several signals to be simultaneously broadcast, each of them being broadcast in a directional lobe of its own. In this figure, 3 Different signals are shown by way of example, but the device can be made with any number of input signals. This number will generally be lower than the number P of the loudspeakers (in the opposite case, the directional lobes would overlap partially). The amplification stage (103, 113, 123, 133) is no longer optional, and in addition each amplifier is an adder that performs the sum of the signals present on its inputs and amplifies this sum.

The signal 1 to be restored is received by a signal processing processor (DSP) which processes it as in the case of the figure 9 . The DSP manufactures using the P digital filters (100, 110, 120, 130) the P filtered versions of the signal 1 to be restored. These filtered versions are delayed by a digital delay line type circuit (101, 111, 121, 131). They are then converted into an analog electrical signal by the converters (102, 112, 122, 132) and these electrical signals are supplied to one of the inputs of the amplifiers (103, 113, 123, 133) performing the sum of their inputs.

The signal 2 to be restored is processed in a similar structure: P digital filters (200, 210, 220, 230) make the P versions which are delayed in the digital delay lines (201, 211, 221, 231), and then converted into analog electrical signals by the converters (202, 212, 222, 232) and presented at the input of the amplifiers (103, 113, 123, 133).

The same is true of the signal 3 to be restored which is processed in a similar structure: P digital filters (300, 310, 320, 330) produce the P versions which are delayed in the digital delay lines (301, 311, 321, 331), then converted into an analog electrical signal by the converters (302, 312, 322, 332) and presented to the input of the amplifiers (103, 113, 123, 133).

The positions of the sensors must respect two contradictory constraints, and the placement of the sensors will result from a compromise between these constraints. First, it is desirable that the spacing between the sensors be half the smallest wavelength

Example: If the maximum frequency present in the signal is f = 7 kHz, and the sound velocity is C = 336 m / s, then the minimum wavelength is λ = C / f -0.048 m. The minimum spacing between sensors shall be 0.024 m for a direction of sight orthogonal to the axis carrying the sensors, and 0.012 m for a direction of sight in the axis of the sensors. These spacings are indicative and may be modified according to constraints related to the physical size of the sensors used.

It is desirable that the sensors are as far apart as possible in order to guarantee the best possible spatial resolution. Typically, the sensors would have to cover a space whose size is several times the largest wavelength in the signal.

Example: if the minimum frequency present in the signal is f = 100 Hz, and if the sound velocity is C = 336 m / s, then the minimum wavelength is λ , = C / f = 3.36 m . The minimum size of the sensor network will be 3.36 m. Such a size will often be incompatible with the actual constraints of the application. This leads to a logarithmic distribution of the sensors.

The figure 1 represents a first example of sensor placement along an axis to form a mono-dimensional network. The spacing of two consecutive microphones (1 to M) obeys a law of logarithmic progression.

We assume here that the sensors are located on a single axis, the sensor m is located at the distance d _m from the origin (by convention, we can say that this origin is located on the sensor 1, which will change these distances, but will not change the distances e _m = d _{m +1} - d _m for m ∈ [1, M -1]). The sensors will be placed in such a way that the ratio between two successive spacings is constant: $$\frac{e_{m+1}}{e_m}=\alpha$$

With the convention that the origin is at the sensor 0 ( d ₁ = 0 ⇒ e ₁ = d ₂ ), the spacing between the first two sensors will be: $$e_1=\frac{{\mathrm{<figure-callout\; id="2"\; label="\lambda \; min"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">\lambda \; </figure-callout>}}_{\min }}{2}$$

Since the size of the network is given by the distance from the sensor numbered M to the first (numbered 1), the spacings between the sensors will have to satisfy the constraint: $$d_M={\displaystyle \underset{m=1}{\overset{M-1}{\Sigma }}}{e}_m$$

The table below illustrates a numerical example of placement of 8 sensors with a ratio α = 1.25 and a spacing of 1 cm between the first 2 sensors. Number of the sensor Distance (cm) Position (cm) 1 1.00 0.00 2 1.25 1.00 3 1.56 2.25 4 1.95 3.81 5 2.44 5.77 6 3.05 8.21 7 3.81 11.26 8 4.77 15.07

An effective embodiment of the device comprises an optimized placement of the sensors. We propose that microphonic sensors be located on a set of rays from a point of origin.

The figure 2 shows the placement of the sensors in this configuration. Two examples are illustrated (12 sensors distributed over 3 radii, and 16 sensors distributed over 5 radii, with a sensor in the center). The first example can be used to form 6 lanes pointing in the 0 °, 60 °, 120 °, 180 °, 240 ° and 300 ° directions. The second example can be used to form 5 lanes pointing to 0 °, 30 °, 110 °, 250 ° directions and 330 °, which are the preferred directions for the reproduction of surround signals, or 5.1.

Another possible embodiment of the device consists of placing the sensors on a circle or on several concentric circles. We can then choose to distribute them evenly on each circle. So if we have Q circles, and if the circle q counts M _q sensors, the angular difference between two successive sensors on this circle will be constant and equal to: $$\frac{2\mathit{\pi }}{M_q}\mathrm{.}$$

The speakers are located on a spoke from an origin point. We will advantageously choose a common origin for the spokes carrying the microphonic sensors, and for the spoke carrying the speakers.

The figure 3 shows the placement of the sensors in this configuration.

Microphonic sensors can also be on hyperbolas. In the case where the number of loudspeakers is P = 2, each sensor can be located in such a way that the difference between the distance d ₁ from the sensor to the loudspeaker 1 and the distance d ₂ from the sensor to the loudspeaker 2 is equal to a constant (identical for all the sensors) noted δ: $$d_{\mathit{1}}-{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">d</figure-callout>}}_{\mathit{2}}=\delta$$

The sensors are then located on a hyperboloide whose speakers 1 and 2 are the homes. To simplify the construction of the device, it is also possible, in this case, to place the sensors on plans containing the two loudspeakers.

The figure 4 illustrates the placement of sensors in this configuration. The two speakers h ₁ and h ₂ are located on a vertical line. The sensors c ₁ and following (in this drawing, c ₁ to c ₆ ) are placed both on a plane passing through the vertical line carrying the two loudspeakers, and in this plane, on the hyperbole of foci h ₁ and h ₂ , such that the condition d ₁ - d ₂ = δ is respected. Other sensors (not numbered in the figure) may be located on one or more other identical hyperbolas, located in other vertical planes passing through the two speakers.

SOUND ENTRY FOR ONE SINGLE EXIT PATH

The processing structure in sound input with a single output channel is represented on the figure 5 .

At the output of the analog-to-digital converters, the signals of the M microphones are denoted x _m (t). After the delay lines, they become: $${\mathrm{there}}_m\left(t\right)=x_m\left(t-{\tau }_m\right),m\in \left[1,M\right]\mathrm{.}$$

Each digital filter (finite impulse response filter of length L) is written: $$z_m\left(t\right)={\displaystyle \underset{k=0}{\overset{\mathrm{The}-1}{\Sigma }}}{h}_m\left(k\right){\mathrm{there}}_m\left(t-k\right),m\in \left[1,M\right]\mathrm{.}$$

At the output of the processing, the unique signal is written: $$s\left(t\right)={\displaystyle \underset{m=1}{\overset{M}{\Sigma }}}{z}_m\left(t\right)\mathrm{.}$$

To perform filter optimization, it is useful to formulate these treatments in the frequency domain.

$${\mathrm{y}}_{\mathrm{m}}\left(\mathrm{t}\right)\to {\mathrm{Y}}_{\mathrm{m}}\left(f\right)$$

$${\mathrm{z}}_{\mathrm{m}}\left(\mathrm{t}\right)\to {\mathrm{Z}}_{\mathrm{m}}\left(f\right)$$

$$\mathrm{s}\left(\mathrm{t}\right)\mathrm{\to }\mathrm{S}\left(\mathit{f}\right)$$

We replace here the time signals by their Fourier transforms: $${\mathrm{x}}_{\mathrm{m}}\left(\mathrm{t}\right)\to {\mathrm{X}}_{\mathrm{m}}\left(f\right)$$

$${\mathrm{there}}_{\mathrm{m}}\left(\mathrm{t}\right)\to {\mathrm{Y}}_{\mathrm{m}}\left(f\right)$$

$${\mathrm{z}}_{\mathrm{m}}\left(\mathrm{t}\right)\to {\mathrm{Z}}_{\mathrm{m}}\left(f\right)$$

$$\mathrm{s}\left(\mathrm{t}\right)\mathrm{\to }\mathrm{S}\left(\mathit{f}\right)$$

$$Z_m\left(f\right)=H_m\left(f\right)Y_m\left(f\right),$$

$$S\left(f\right)={\displaystyle \sum _{m=1}^M}{Z}_m\left(f\right)\mathrm{.}$$

The received signals X _m ( f ) are first delayed to give the signals Y _m ( f ) which are then filtered to give the signals Z _m ( f ); these are then summed to give the output S ( f ): $$Y_m=X_m\left(f\right)e^{j2\mathit{\pi f}{\tau }_m}$$

$$Z_m\left(f\right)=H_m\left(f\right)Y_m\left(f\right),$$

$$S\left(f\right)={\displaystyle \underset{m=1}{\overset{M}{\Sigma }}}{Z}_m\left(f\right)\mathrm{.}$$

We can condense these expressions in the following expression: $$S\left(f\right)={\displaystyle \underset{m=1}{\overset{M}{\Sigma }}}{H}_m\left(f\right)e^{-j2{\mathit{\pi f\tau }}_m}{X}_m\left(f\right)\mathrm{.}$$

Digital delays can be set arbitrarily. An effective realization is to choose them as the entire part of the quotient of the delay (relative to the reference sensor, for the reference direction) over the sampling period

Filter optimization

• identification des réponses du canal acoustique entre une source visée et les capteurs
• optimisation dans le domaine des fréquences des paramètres des filtres, garantissant une réponse donnée pour la source visée, minimisant l'énergie du diagramme de directivité hors du lobe principal, sous deux contraintes d'inégalité, l'une sur le diagramme de directivité sous le lobe, l'autre sur le gain en bruit propre des capteurs
• optimisation dans le domaine temporel des coefficients du filtre approchant au mieux les réponses en fréquence trouvées à l'étape précédente.

The filter optimization procedure we present here breaks down into several phases:

• identification of acoustic channel responses between a target source and the sensors
• optimization in the frequency domain of the parameters of the filters, guaranteeing a given response for the target source, minimizing the energy of the directivity diagram out of the main lobe, under two inequality constraints, one on the directivity diagram under the lobe, the other on the noise gain of the sensors
• optimization in the time domain of the coefficients of the filter approaching the best frequency responses found in the previous step.

These steps are detailed below.

Acoustic characterization

For optimization, it is necessary to identify a number of channel impulse responses acoustic. One possible technique is to place a speaker at the source, transmit a pseudo-random bit sequence, collect the signal on the sensor, calculate the cross-correlation between the pseudo-random bit sequence and the collected signal. Intercorrelation then constitutes a measure of the impulse response sought.

FREQUENCY OPTIMIZATION CRITERIA

• la direction de la source visée,
• les directions des sources qui se situent à l'intérieur d'un voisinage, ce sont les directions qui définissent le lobe principal du diagramme de directivité ;
• les directions des sources à rejeter, (il importe que le cardinal de cet ensemble soit supérieur au nombre de capteurs).

Filter optimization is done from a set of directions:

• the direction of the intended source,
• the directions of the sources which are located within a neighborhood, it is the directions which define the main lobe of the directivity diagram;
• the directions of the sources to reject, (it is important that the cardinal of this set is greater than the number of sensors).

If a source is in one of the neighborhood directions, it will be received with a gain close to 1 (usually slightly less than 1). If a source is in one of the directions to reject, it will be processed to have a very small gain.

We also define a reference frequency; below this frequency, the optimization will be done without constraints on the neighborhood set, while above this frequency, we will introduce an additional constraint on the directions of the sources to be rejected.

Constraint in the aiming direction

The optimization of the filters is done under the constraint that the directivity diagram has value 1 in the direction of the targeted source.

MINIMIZATION OF SECONDARY LOBES

Our filter optimization criterion is based on eliminating signals that are outside the zone the space where the main lobe of the network will be located. This zone is defined a priori. It will depend on the specifications of the application. To reject as much as possible the sources that lie in these directions, we minimize the sum of squares of the amplitudes of the directivity diagram in these directions.

CONSTRAINTS IN THE MAIN LOBE

For all the directions lying in the main lobe, when the frequency is above the reference frequency, we will impose a set of inequality constraints.

The purpose of these constraints is to allow the directivity pattern to keep a constant shape for all frequencies above the reference frequency. Without this constraint, the minimization of the criterion J would lead to values of the directivity diagram that would be greater than 1 for the directions in the region.

CONSTRAINT ON THE GAIN IN CLEAN NOISE

The sensors are all affected by a noise, called clean noise, which comes from the operation of the sensor itself and not sounds picked up. The processing of the signals picked up in our device may increase the noise level of the sensors. We need to control this level, setting a maximum value for the amplification gain of the sensors own noise.

To calculate the noise gain of the device, we must assume that we receive on the one hand a useful signal from a source in the direction of θ and on the other hand the own noise of the sensors. This situation is summarized by the Figure 12 .

The received signal is the sum of two signals, that corresponding to the source Y _u (f) and that corresponding to the noise Y _B (f): $$\mathrm{Y}\left(\mathrm{f}\right)\mathrm{=}{\mathrm{Y}}_{\mathrm{b}}\left(\mathrm{f}\right)\mathrm{+}{\mathrm{Y}}_{\mathrm{u}}\left(\mathrm{f}\right)\mathrm{.}$$

The signal received from the useful source is expressed as the signal U (f) propagating in the channel whose frequency response is C _θ (f), then amplified by the gain of the sensors G ( f ) and finally delayed on each sensor, which represents the matrix V (f), before being treated by the filters H (f): $${\mathbf{Y}}_{\mathrm{u}}\left(\mathrm{f}\right)\mathrm{=}\mathbf{H}{\left(\mathrm{f}\right)}^{\mathrm{H}}\mathbf{V}\left(\mathrm{f}\right)\mathbf{BOY\; WUT}\left(\mathrm{f}\right){\mathbf{VS}}_{\mathrm{\theta }}\left(\mathrm{f}\right)\mathrm{U}\left(\mathrm{f}\right)$$

The noise of the sensors does not propagate in the acoustic channel, being born inside the sensor, but it is also amplified by the gain of the sensors, delayed on each sensor, which represents the matrix V (f), before being treated by the filters H (f).

SOUND ENTRY WITH MULTIPLE OUTPUT PATH Structure

The output channels are indexed by n ∈ [1, N ].

To produce the output S _n (t), we apply the delays τ _n , _m ; after the delay lines, the captured signals become: $${\mathrm{there}}_{\mathrm{not}\mathrm{,}\mathrm{m}}\left(\mathrm{t}\right)\mathrm{=}{\mathrm{x}}_{\mathrm{m}}\left(\mathrm{t}\mathrm{-}{\mathrm{\tau }}_{\mathrm{not}\mathrm{,}\mathrm{m}}\right)m\in \left[1,M\right],\mathrm{not}\in \left[1,\mathrm{NOT}\right]\mathrm{.}$$

Each signal y _{n, m} (t), m ∈ [1, M ], n ∈ [1, N ] is filtered by a digital filter (finite impulse response filter of length L ) and the result is written: $$z_{\mathrm{not},m}\left(t\right)={\displaystyle \underset{k=0}{\overset{\mathrm{The}-1}{\Sigma }}}{h}_{\mathrm{not},m}\left(k\right){\mathrm{there}}_{\mathrm{not},m}\left(t-k\right),m\in \left[1,M\right],\mathrm{not}\in \left[1,\mathrm{NOT}\right]\mathrm{.}$$

At the output of the processing, the signal of the output channel n is written: $$s_{\mathrm{not}}\left(t\right)={\displaystyle \underset{m=1}{\overset{M}{\Sigma }}}{z}_{\mathrm{not},m}\left(t\right)\mathrm{.}$$

This treatment structure is represented on the figure 6 .

Selection of exit routes

When the acquisition is done on N channels in parallel, one extracts from these N channels a single channel which will be the signal coming out of the device (for example in a videoconferencing or audio conferencing application, this will be the signal that after compression will be sent to the distant correspondent).

Here we consider two variants, one based on the selection of the combination of signals giving the maximum energy output, the other on the identification of the direction of arrival of the dominant signal followed by the construction. of the corresponding output signal (by weighting between two of the N outputs).

Selection by optimization of the output energy

The objective is to reconstruct a signal s (t) by linear combination between the signals s _n (t), n ∈ [1, N ]. The chosen combination will be noted: $$s\left(t\right)={\displaystyle \underset{\mathrm{not}=1}{\overset{\mathrm{NOT}}{\Sigma }}}{w}_{\mathrm{not}}\left(t\right)s_{\mathrm{not}}\left(t\right)$$

dans lequel la matrice R _t est la covariance des N signaux s_n(t), n ∈ [1, N]., réunis dans le vecteur S_t : $$R_t={\displaystyle \sum _{\tau \le t}}{S}_{\tau }{S}_{\tau }^T\mathrm{avec}{S}_t=\lfloor \begin{array}{c}{s}_1\left(t\right)\\ s_2\left(t\right)\\ ⋮\\ s_N\left(t\right)\end{array}\rfloor ,$$

et le vecteur W_t regroupe les poids w_n(t) : $$W_t=\lfloor \begin{array}{c}{w}_1\left(t\right)\\ w_2\left(t\right)\\ ⋮\\ w_N\left(t\right)\end{array}\rfloor \mathrm{.}$$

In this writing, the weights w _n ( t ) that affect each of the N signals s _n (t), n ∈ [1, N ] are variable over time. To determine optimal weights at each moment, we maximize the criterion: $$\underset{W_t}{\mathrm{Low}}{W}_t^T{R}_t{W}_t,$$

in which the matrix R _t is the covariance of the N signals s _n (t), n ∈ [1, N ]., gathered in the vector S _t : $$R_t={\displaystyle \underset{\tau \le t}{\Sigma }}{S}_{\tau }{S}_{\tau }^T\mathrm{with}{S}_t=\lfloor \begin{array}{c}{s}_1\left(t\right)\\ s_2\left(t\right)\\ ⋮\\ s_{\mathrm{NOT}}\left(t\right)\end{array}\rfloor ,$$

and the vector W _t groups the weights w _n ( t ): $$W_t=\lfloor \begin{array}{c}{w}_1\left(t\right)\\ w_2\left(t\right)\\ ⋮\\ w_{\mathrm{NOT}}\left(t\right)\end{array}\rfloor \mathrm{.}$$

The minimization is done under the constraint that the vector W _t has a norm equal to 1.

avec ${\mathit{Grad}}_{W_t}{W}_t^T{R}_t{W}_t=2R_t{W}_t,$

soit encore : W̃ _t+1 =W_t +2µ R_tW_t. We recursively minimize this criterion, using a gradient algorithm, which gives us a non-normalized estimate of W _{t +1} : $${\stackrel{}{W}}_{t+1}=W_t+\mu {\mathit{Grad}}_{W_t}{W}_t^T{R}_t{W}_t,$$

with ${\mathit{Grad}}_{W_t}{W}_t^T{R}_t{W}_t=2R_t{W}_t,$

again: W _{t +1} = W _t + 2μ R _t W _t .

soit encore W̃ _t+1 = W_t +2µ S_ts(t)Another estimate of the gradient is obtained by replacing the matrix R _t by an instantaneous estimate, which leads to: $${\stackrel{}{W}}_{t+1}=W_t+2\mu S_t\left(S_t^T{W}_t\right),$$

let W _{t +1} = W _t + 2μ S _t s ( t )

We will then normalize the estimation W _{t +1} to obtain the estimate of W _{t +1} : $$W_{t+1}=\frac{{\stackrel{}{W}}_{t+1}}{\sqrt{{\stackrel{}{W}}_{t+1}^T{\stackrel{}{W}}_{t+1}}}$$

This treatment structure is represented on the figure 7 .

Selection by identification of the position of the source.

The identification of the position of the source can be done by conventional methods, for example that presented by Y.Grenier, P.Loubaton, "Localization of broadband sources by temporal methods", 12th Symposium on Signal Processing and its Applications, GRETSI, Juan-les-Pins, pp 457-460, 1989 .

Each output channel is associated with a direction (generally the direction in which the reception level is maximum). If we assume that the direction θ of the source lies between the directions associated with the channels n and ( n +1), the source will be received on these two channels with respective gains that depend on the directivity diagram in θ of the two channels of reception, according to the two equations below: $$S_{\mathrm{not}}\left(f\right)={\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)E\left(f\right)\mathrm{and}{S}_{\mathrm{not}+1}\left(f\right)={\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)E\left(f\right)\mathrm{.}$$

This can still be written in matrix form: $$\lfloor \begin{array}{c}{S}_{\mathrm{not}}\left(f\right)\\ S_{\mathrm{not}+1}\left(f\right)\end{array}\rfloor =\lfloor \begin{array}{c}{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)\\ {\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)\end{array}\rfloor E\left(f\right)\mathrm{.}$$

If we are looking for an output signal S ( f ) which approaches the signal E ( f ) emitted by the source, it is natural to try to minimize the energy of the difference between the signals observed, and those which should give this signal S ( f ), that is, minimize the quantity: $${\left|\left[\begin{array}{c}{S}_{\mathrm{not}}\left(f\right)\\ S_{\mathrm{not}+1}\left(f\right)\end{array}\right]-\left[\begin{array}{c}{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)\\ {\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)\end{array}\right]\mathrm{<figure-callout\; id="2"\; label="S\; f"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">S\; </figure-callout>}\left(f\right)\left(\right)\right|}^2\mathrm{.}$$

expression dans laquelle A^H désigne le conjugué transposé de la matrice A. Cette expression peut aussi s'écrire (en posant que A* est le conjugué de A) : $$S\left(f\right)=\frac{G_{n,\theta }\left(f\right)*S_n\left(f\right)+G_{n+1,\theta }\left(f\right)*S_{n+1}\left(f\right)}{G_{n,\theta }\left(f\right)*G_{n,\theta }\left(f\right)+G_{n+1,\theta }\left(f\right)*G_{n+1,\theta }\left(f\right)},$$

soit encore $$S\left(f\right)=L_{n,\theta }\left(f\right)S_n\left(f\right)+L_{n+1,\theta }\left(f\right)S_{n+1}\left(f\right)$$

avec $$L_{n,\theta }\left(f\right)=\frac{G_{n,\theta }{\left(f\right)}^{*}}{G_{n,\theta }{\left(f\right)}^{*}{G}_{n,\theta }\left(f\right)+G_{n+1,\theta }{\left(f\right)}^{*}{G}_{n+1,\theta }\left(f\right)},$$

et $$L_{n+1,\theta }\left(f\right)=\frac{G_{n+1,\theta }{\left(f\right)}^{*}}{G_{n,\theta }{\left(f\right)}^{*}{G}_{n,\theta }\left(f\right)+G_{n+1,\theta }{\left(f\right)}^{*}{G}_{n+1,\theta }\left(f\right)}$$

The solution is calculated as: $$S\left(f\right)={\left({\left[\begin{array}{c}{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)\\ {\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)\end{array}\right]}^H\left[\begin{array}{c}{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)\\ {\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)\end{array}\right]\right)}^{-1}{\left[\begin{array}{c}{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)\\ {\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)\end{array}\right]}^H\left[\begin{array}{c}{S}_{\mathrm{not}}\left(f\right)\\ S_{\mathrm{not}+1}\left(f\right)\end{array}\right],$$

where A ^H is the transposed conjugate of template A. This expression can also be written (by asking that A * is the conjugate of A ): $$S\left(f\right)=\frac{{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)*S_{\mathrm{not}}\left(f\right)+{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)*S_{\mathrm{not}+1}\left(f\right)}{{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)*{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)+{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)*{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)},$$

is still $$S\left(f\right)={\mathrm{The}}_{\mathrm{not},\theta }\left(f\right)S_{\mathrm{not}}\left(f\right)+{\mathrm{The}}_{\mathrm{not}+1,\theta }\left(f\right)S_{\mathrm{not}+1}\left(f\right)$$

with $${\mathrm{The}}_{\mathrm{not},\theta }\left(f\right)=\frac{{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }{\left(f\right)}^{*}}{{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }{\left(f\right)}^{*}{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)+{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }{\left(f\right)}^{*}{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)},$$

and $${\mathrm{The}}_{\mathrm{not}+1,\theta }\left(f\right)=\frac{{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }{\left(f\right)}^{*}}{{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }{\left(f\right)}^{*}{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)+{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }{\left(f\right)}^{*}{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)}$$

This last expression suggests that the functions L _{n, θ} ( f ) and L _{n + 1, θ} ( f ) are tabulated for a set of values of θ regularly distributed between 0 and 2π radians. More precisely, l _{n , θ} ( t ) and l _{n + 1 , θ} ( t ), which are the respective inverse Fourier transforms of L _{n , θ} ( f ) and L _{n + 1, θ} ( f ), will be tabulated .

This treatment structure is represented on the figure 8 .

avec la notation : $$\langle a\left(f\right)|b\left(f\right)\rangle =\underset{\mathrm{-}\frac{\mathrm{1}}{\mathrm{2}}}{\overset{\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{\int }}}a{\left(f\right)}^{*}b\left(f\right)\mathit{df}\mathrm{.}$$

A simplified version is obtained by assuming that the functions L _{n, θ} ( f ) and L _{n + 1, θ} ( f ) are independent of the frequency and reduced to two gains L _{n, θ} and L _{n + 1, θ} . The minimization of the criterion is done then on all the frequencies and not more frequency by frequency. The two gains are then solution of: $$\lfloor \begin{array}{cc}<{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)|{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)>& <{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)|{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)>\\ <{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)|{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)>& <{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)|{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)>\end{array}\rfloor \left[\begin{array}{c}{\mathrm{The}}_{\mathrm{not},\theta }\\ {\mathrm{The}}_{\mathrm{not}+1,\theta }\end{array}\right]=\lfloor \begin{array}{c}<\begin{array}{c}{\mathrm{BOY\; WUT}}_{\mathrm{not},\theta }\left(f\right)|1\end{array}>\\ <\begin{array}{c}{\mathrm{BOY\; WUT}}_{\mathrm{not}+1,\theta }\left(f\right)\end{array}|1>\end{array}\rfloor ,$$

with the notation: $$<\mathrm{at}\left(f\right)|b\left(f\right)>=\underset{\mathrm{-}\frac{\mathrm{1}}{\mathrm{2}}}{\overset{\frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{\int }}}\mathrm{at}{\left(f\right)}^{*}b\left(f\right)\mathit{df}\mathrm{.}$$

RESTITUTION OF SOUND Structure

The signal to be restored is written: r (t). We make P shifted versions, denoted u _P (t), p ∈ [1, P ] and with delays τ _p : $$u_p\left(t\right)=r\left(t-{\stackrel{}{\tau }}_p\right),p\in \left[1,P\right]\mathrm{.}$$

These signals are then filtered and the results of these filterings, noted v _p ( t ) will then be restored by the loudspeakers (after digital-to-analog conversion): $$v_p\left(t\right)={\displaystyle \underset{k=0}{\overset{\stackrel{}{\mathrm{The}}-1}{\Sigma }}}{\mathrm{boy\; Wut}}_p\left(k\right)u_p\left(t-k\right),p\in \left[1,P\right]\mathrm{.}$$

This treatment structure is represented on the figure 9 .

Directivity diagram

$$u_p\left(t\right)\to U_p\left(f\right),$$

$$v_p\left(t\right)\to V_p\left(f\right),$$

$${\stackrel{}{r}}_{\theta }\left(t\right)\to {\stackrel{}{R}}_{\theta }\left(f\right)\mathrm{.}$$

To obtain the directivity diagram in restitution, we proceed as in the case of the acquisition. We replace the signals by their Fourier transforms: $$r\left(t\right)\to R\left(f\right),$$

$$u_p\left(t\right)\to U_p\left(f\right),$$

$$v_p\left(t\right)\to V_p\left(f\right),$$

$${\stackrel{}{r}}_{\theta }\left(t\right)\to {\stackrel{}{R}}_{\theta }\left(f\right)\mathrm{.}$$

soit en revenant aux signaux décalés, avant filtrage, U_p (f) : $${\stackrel{}{R}}_{\theta }\left(f\right)={\displaystyle \sum _{p=1}^P}{\stackrel{}{C}}_{p,\theta }\left(f\right){\stackrel{}{H}}_p\left(f\right)U_p\left(f\right),$$

puis en revenant au signal à restituer R (f) : $${\stackrel{}{R}}_{\theta }\left(f\right)={\displaystyle \sum _{p=1}^P}{\stackrel{}{C}}_{p,\theta }\left(f\right){\stackrel{}{H}}_p\left(f\right)e^{-j2\mathit{\pi f}{\stackrel{}{\tau }}_p}R\left(f\right)\mathrm{.}$$

The signal to be reproduced R ( f ) is converted into P offset versions U _p ( f ), which are then filtered to give the signals V _P ( f ) which will be restored. At a point whose position is indicated by θ, the received signal R _θ ( f ) is the sum of the contributions of these P restored signals filtered by the corresponding acoustic channel C _{p , θ} ( f ) (channel between the loudspeaker p and the measuring point at position θ): $${\stackrel{}{R}}_{\theta }\left(f\right)={\displaystyle \underset{p=1}{\overset{P}{\Sigma }}}{\stackrel{}{\mathrm{VS}}}_{p,\theta }\left(f\right)V_p\left(f\right),$$

either by returning to the shifted signals, before filtering, U _p ( f ): $${\stackrel{}{R}}_{\theta }\left(f\right)={\displaystyle \underset{p=1}{\overset{P}{\Sigma }}}{\stackrel{}{\mathrm{VS}}}_{p,\theta }\left(f\right){\stackrel{}{H}}_p\left(f\right)U_p\left(f\right),$$

then returning to the signal to restore R ( f ): $${\stackrel{}{R}}_{\theta }\left(f\right)={\displaystyle \underset{p=1}{\overset{P}{\Sigma }}}{\stackrel{}{\mathrm{VS}}}_{p,\theta }\left(f\right){\stackrel{}{H}}_p\left(f\right)e^{-j2\mathit{\pi f}{\stackrel{}{\tau }}_p}R\left(f\right)\mathrm{.}$$

Frequency optimization criterion (restitution)

The optimization of the rendering device resembles that of the acquisition device. The starting point is the expression of the directivity diagram: $${\stackrel{}{D}}_{\theta }\left(f\right)={\stackrel{}{\mathbf{H}}}^H\left(f\right)\stackrel{}{\mathbf{V}}\left(f\right)\stackrel{}{\mathbf{BOY\; WUT}}\left(f\right){\stackrel{}{\mathbf{VS}}}_{\theta }\left(f\right)\mathrm{.}$$

Where G ( f ) is the gain of the loudspeaker at frequency f .

• la direction de restitution préférée,
• les directions de restitution qui se situent à l'intérieur d'un voisinage, constitué par les directions qui définissent le lobe principal du diagramme de directivité,
• les directions des sources à rejeter, (il importe que le cardinal de cet ensemble soit supérieur au nombre de haut-parleurs).

Filter optimization is done from a set of directions:

• the preferred direction of restitution,
• restitution directions which are located within a neighborhood, constituted by the directions that define the main lobe of the directivity pattern,
• the directions of the sources to reject, (it is important that the cardinal of this set is greater than the number of speakers).

The optimization of the filters is done under the constraint that the directivity diagram has value 1 in the direction of the targeted source.

Minimization of side lobes

Our criteria for optimizing filters is based on the absence of restitution of signals outside the area of the space where the main lobe of the network will be located. This zone is defined a priori. It will depend on the specifications of the application. It will be represented by the directions of the set Θ ₂ . For this, we minimize the sum of squares of the amplitudes of the directivity diagram in these directions.

Constraints in the main lobe

et nous imposerons : $${\Vert \stackrel{}{\mathbf{H}}{\left(f\right)}^H\stackrel{}{V}\left(f\right)\stackrel{}{\mathbf{G}}\left(f\right){\stackrel{}{\mathbf{C}}}_{\theta }\left(f\right)\Vert }^2\le {\stackrel{}{\alpha }}_{\theta };\theta \in {\stackrel{}{\mathrm{\Theta }}}_1\mathrm{.}$$

For all the directions lying in the main lobe, when the frequency f is above the reference frequency, a set of inequality constraints is imposed. We will define for this a set of values: $$\left\{{\stackrel{}{\alpha }}_{\theta };\theta \in {\stackrel{}{\mathrm{\Theta }}}_1\right\},$$

and we will impose: $${\Vert \stackrel{}{\mathbf{H}}{\left(f\right)}^H\stackrel{}{V}\left(f\right)\stackrel{}{\mathbf{BOY\; WUT}}\left(f\right){\stackrel{}{\mathbf{VS}}}_{\theta }\left(f\right)\Vert }^2\le {\stackrel{}{\alpha }}_{\theta };\theta \in {\stackrel{}{\mathrm{<figure-callout\; id="1"\; label="\Theta "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\Theta </figure-callout>}}}_1\mathrm{.}$$

The choice of the terminals α _θ will generally be made by making them equal to the squares of the amplitude of the directivity diagram at the reference frequency f _r : $${\stackrel{}{\alpha }}_{\theta }={\Vert \stackrel{}{\mathbf{H}}{\left(f_r\right)}^H\stackrel{}{\mathrm{V}}\left(f_r\right)\stackrel{}{\mathbf{BOY\; WUT}}\left(f_r\right){\stackrel{}{\mathbf{VS}}}_{\theta }\left(f_r\right)\Vert }^2\mathrm{for}\theta \in {\stackrel{}{\mathrm{<figure-callout\; id="1"\; label="\Theta "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\Theta </figure-callout>}}}_1$$

The purpose of these constraints is to allow the directivity pattern to keep a constant shape for all frequencies above the reference frequency.

Optimization

We do not impose a constraint on the noise of the loudspeakers, because this noise will not be affected by the treatments performed, unlike what happened in the case of the acquisition.

sous les contraintes linéaires H̃(f) ^H Ṽ(f)G̃(f)C̃ _θ̃o(f)=1,
auxquelles s'ajoutent, si f ≥ f_r, les contraintes quadratiques : $${\Vert \stackrel{}{\mathbf{H}}{\left(f\right)}^H\stackrel{}{\mathbf{V}}\left(f\right)\stackrel{}{\mathbf{G}}\left(f\right){\stackrel{}{\mathbf{C}}}_{\theta }\left(f\right)\Vert }^2\le {\Vert \stackrel{}{\mathbf{H}}{\left(f_r\right)}^H\stackrel{}{\mathbf{V}}\left(f_r\right)\stackrel{}{\mathbf{G}}\left(f_r\right){\stackrel{}{\mathbf{C}}}_{\theta }\left(f_r\right)\Vert }^2\mathrm{pour}\theta \in {\stackrel{}{\mathrm{\Theta }}}_1\mathrm{.}$$

The algorithm thus becomes: $$\mathrm{Minimize}J=\stackrel{}{\mathbf{H}}{\left(f\right)}^H{\mathbf{<figure-callout\; id="3"\; label="R"\; filenames="imgf0001.png,imgf0006.png"\; state="\{\{state\}\}">R</figure-callout>}}_3\stackrel{}{\mathbf{H}}\left(f\right),$$

under the linear constraints H ( f ) ^H Ṽ ( f ) G ( f ) C _{θ 0} ( f ) = 1,
to which are added, if f ≥ f _r , the quadratic constraints: $${\Vert \stackrel{}{\mathbf{H}}{\left(f\right)}^H\stackrel{}{\mathbf{V}}\left(f\right)\stackrel{}{\mathbf{BOY\; WUT}}\left(f\right){\stackrel{}{\mathbf{VS}}}_{\theta }\left(f\right)\Vert }^2\le {\Vert \stackrel{}{\mathbf{H}}{\left(f_r\right)}^H\stackrel{}{\mathbf{V}}\left(f_r\right)\stackrel{}{\mathbf{BOY\; WUT}}\left(f_r\right){\stackrel{}{\mathbf{VS}}}_{\theta }\left(f_r\right)\Vert }^2\mathrm{for}\theta \in {\stackrel{}{\mathrm{<figure-callout\; id="1"\; label="\Theta "\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">\Theta </figure-callout>}}}_1\mathrm{.}$$

Restitution of several signals

When several signals are to be reproduced simultaneously, each by its directional lobe, using a structure such as that illustrated by the figure 13 in the case of 3 signals,

• la direction de restitution préférée,
• les directions de l'ensemble ⊝̃₂(K) qui représentent la zone de l'espace en dehors du lobe principal,
• les directions de l'ensemble Θ̃₁(K) dans le lobe principal et les valeurs des bornes α̃_θ dans les directions de cet ensemble.

the optimization will lead for each signal to a filter H ( f ). The filter will be optimized independently of the filters ensuring the diffusion of the other signals. For example, for the signal K to be restored, filters H _K ( f ) will be calculated. To calculate the filters H K ( f ), we will define:

• the preferred direction of restitution,
• the directions of the set ⊝ ₂ ( K ) which represent the area of the space outside the main lobe,
• the directions of the set Θ ₁ ( K ) in the main lobe and the values of the terminals α _θ in the directions of this set.

It is not necessary to calculate the filters HK ( f ) to take into account the other filters.
Thanks to the amplifiers that sum the analog signals, the directivity diagrams apply to each of the signals to be rendered.

JOINT ENTRY AND RESTITUTION Cancellation of acoustic echoes

The device comprising both the acquisition and the restitution of the sounds, an acoustic coupling occurs between the restitution part and the acquisition part. Therefore, the signal output from the speakers will be picked up by the microphones. This is the phenomenon of acoustic echo, well described in the article of B.Widrow et al., Adaptive Noise Canceling: Principles and Application, Proc. of IEEE, Vol.63, No. 12, pp 1692-1716, 1975 . It shows in particular the possibility of establishing an acoustic echo canceller on the basis of an algorithm called "LMS". Another echo cancellation algorithm, more efficient, was presented in the article E.Moulines, O.Ait Amrane, Y.Grenier, "The Generalized Multi-delay Adaptive Filter: Structure and Convergence Analysis.", IEEE Trans. On Signal Processing, Vol.43, No. 1, pp 14-18, January 1995 .

In our device, we will include an echo canceller (for example of one of the types mentioned above), between the signal to be restored and the signal picked up. The acoustic echo canceller is rated AEC in the diagrams (AEC refers to Acoustic Echo Canceller). The figure 10 shows a complete view of the device, including sound acquisition with an output channel (as in figure 5 ), an acoustic echo cancellation block, the sound reproduction as in the figure 9 , and a mixing block as in the figure 7 or the figure 8 .

When we perform channel acquisition with multiple simultaneous outputs, it would be possible to incorporate the mixing between the acquisition and an echo canceller operating on a single channel. We prefer to insert as many echo cancellers as output channels: these cancellers use the same "loudspeaker" signal, and each of them cancels the echo of this signal to be restored in each of the output channels, before to provide this echo-free signal to the block ensuring the selection (or mixing) of the signals. The figure 11 shows a complete view of the device, including sound acquisition with multiple output channels (as in figure 6 ), an acoustic echo cancellation block, the sound reproduction as in the figure 9 , and a mixing block as in the figure 7 or the figure 8 .

Criteria for joint optimization in frequency

When the device performs both acquisition and restitution, the two criteria are modified to take account of this situation. Thus, the optimization of the acquisition will have an additional goal: cancel the signals received from the speaker. Similarly, the optimization of the restitution will have the additional goal of not returning the signal to the sensors for acquisition.

Note C _{m, p} ( f ) the transfer function (Fourier transform of the impulse response) of the acoustic channel between the sensor m and the loudspeaker p .

Additional constraints in acquisition

$$\mathrm{où}{\mathbf{C}}_p\left(f\right)=\lfloor \begin{array}{c}{C}_{1,p}\left(f\right)\\ C_{2,p}\left(f\right)\\ ⋮\\ C_{M,p}\left(f\right)\end{array}\rfloor \mathrm{.}$$

For the acquisition, the filters H _m ( f ) will have to check the following P constraints: $$\mathbf{H}{\left(f\right)}^H\mathbf{V}\left(f\right)\mathbf{BOY\; WUT}\left(f\right){\mathbf{VS}}_p\left(f\right)=0,p\in \left[1,P\right],$$

$$\mathrm{or}{\mathbf{VS}}_p\left(f\right)=\lfloor \begin{array}{c}{\mathrm{VS}}_{1,p}\left(f\right)\\ {\mathrm{VS}}_{2,p}\left(f\right)\\ ⋮\\ {\mathrm{VS}}_{M,p}\left(f\right)\end{array}\rfloor \mathrm{.}$$

Additional constraints in restitution

où $${\stackrel{}{\mathbf{C}}}_m\left(f\right)=\lfloor \begin{array}{c}{C}_{m,1}\left(f\right)\\ C_{m,2}\left(f\right)\\ ⋮\\ C_{m,P}\left(f\right)\end{array}\rfloor \mathrm{.}$$

For the restitution, the filters H _m ( f ) will have to check the following M constraints: $$\stackrel{}{\mathbf{H}}{\left(f\right)}^H\stackrel{}{\mathbf{V}}\left(f\right)\stackrel{}{\mathbf{BOY\; WUT}}\left(f\right){\stackrel{}{\mathbf{VS}}}_m\left(f\right)=0,m\in \left[1,M\right],$$

or $${\stackrel{}{\mathbf{VS}}}_m\left(f\right)=\lfloor \begin{array}{c}{\mathrm{VS}}_{m,1}\left(f\right)\\ {\mathrm{VS}}_{m,2}\left(f\right)\\ ⋮\\ {\mathrm{VS}}_{m,P}\left(f\right)\end{array}\rfloor \mathrm{.}$$

The passage in time remains unchanged.

Claims (11)

1. System for processing a sound signal having at least one directive or main lobe and comprising at least one amplifier, an analogue to digital conversion circuit or a digital to analogue conversion circuit, a digital filtering circuit, end-processing elements and a circuit for adding the signals filtered by the filtering circuit so as to deliver at least one output signal, said end-processing elements being sound sensors, the filtering circuit being optimised according to the inherent characteristics of the end-processing elements and according to the geometric location thereof; an optimisation broken down according to at least the following phases:

   - identification of the responses of the acoustic channel between a source aimed at and the sensors,

   - optimisation in the frequency domain of the parameters of the filters guaranteeing a given response for the source aimed at, minimising the energy of the directivity diagram outside the main lobe, under two inequality constraints, one on the directivity diagram under the lobe, the other on the inherent noise gain of the sensors,

   - optimisation in the time domain of the coefficients of the filter best approximating the frequency responses found at the previous phase,
   and an output circuit delivering one output signal per directive lobe, the system being characterised in that the output circuit is arranged to deliver several directive output signals s_n(t) each corresponding to a directive lobe "n", a system for which said adding circuit is arranged to recompose these various output signals with a view to forming, for use purposes, a single signal s(t) corresponding to a linear combination of the directive output signals in the form:
   $s\left(t\right){\displaystyle \sum _n}{w}_n\left(t\right)\mathrm{.}{s}_n\left(t\right),$

   

   the weighting factors w_n(t) being variable over time and satisfying the constraint
   ${\displaystyle \sum _{n=1}^N}{w}_n^2\left(t\right)=1,$

   

   N being the number of lobes.
2. System for processing a sound signal according to claim 1, in which the sound sensors are distributed on a plurality of axes having the same point of origin.
3. System for processing a sound signal according to any of claims 1 to 2, wherein the sound sensors are distributed on a plurality of coplanar axes.
4. System for processing a sound signal according to any of claims 1 to 3, wherein the sound sensors are distributed on three axes forming an angle of 120° with each other.
5. System for processing a sound signal according to any one of claims 1 to 3, in which the sounds sensors are distributed on five axes oriented respectively with an angle of 0°, 1 30° or + 110° with respect to a reference axis.
6. System for processing a sound signal according to claim 1, wherein each weighting factor w _n (t) is the energy of the corresponding lobe n.
7. System for processing a sound signal according to claim 1, further arranged so that, when a sound source producing the sound signal is situated in a direction θ situated between the directions of a first lobe n and a second lobe n+1, the single signal s(t) is, in the frequency domain, such that: $$S\left(\mathrm{f}\right)=L_{n,0}\left(f\right)S_n\left(f\right)+L_{n+1,0}\left(f\right)S_{n+1}\left(f\right)$$

   

   
   where:
   S(f) designates the amplitude of the output signal as a function of the frequency,
   L _n0(f) designates, in the frequency domain, the weighting factor w_n(t) that is a function of the identifier of the first lobe and of the angle of the source,
   Ln=_1.0(f) designates, in the frequency domain, the weighting factor w_n(t) that is a function of the identifier of the second lobe and of the angle of the source,
   S(f) designates, in the frequency domain, the amplitude of the signal of the first lobe,
   S _n+1(f) designates, in the frequency domain, the amplitude of the signal of the second lobe.
8. System for processing a sound signal according to any of the preceding claims, further comprising loudspeakers arranged to reproduce a sound, the system further comprising acquisition filters and reproduction filters.
9. System for processing a sound signal according to claim 8, in which:

   - the acquisition filters are defined by:
   H_m(f) such that H(f)^HV(f)G(f) C_p(f)=0,p ∈ [1,P] with: $C_p\left(f\right)\left[\begin{array}{l}{C}_{1,p}\left(f\right)\\ C_{2,p}\left(f\right)\\ \cdot \\ \cdot \\ \cdot \\ C_{M,p}\left(f\right)\end{array}\right],$

   

   C_mp (f) designating the Fourier transform of the pulse response of the acoustic channel between the sensor m and the loudspeaker p, P being the total number of loudspeakers and M being the total number of sound sensors,
   
   H(f)^H being the transposed conjugate of the matrix H(f) representing the filter H_m(f), the vector V(f) representing the filtered signals and the vector G(f) the gain,

   - and the reproduction filters by: H̃ _m(f) such that: $$\stackrel{}{\mathbf{H}}{\left(\mathbf{f}\right)}^{\mathbf{H}}\stackrel{}{\mathbf{V}}\left(\mathbf{f}\right)\stackrel{}{\mathbf{G}}\left(\mathbf{f}\right){\stackrel{}{\mathbf{C}}}_{\mathbf{m}}\left(\mathit{f}\right)=0,m\in \left[1,M\right]$$

   

   $${\stackrel{}{C}}_m\left(f\right)\left[\begin{array}{l}{C}_{1,p}\left(f\right)\\ C_{1,9}\left(f\right)\\ \cdot \\ \cdot \\ \cdot \\ C_{M,p}\left(f\right)\end{array}\right]$$

   

   
   so that the reproduction filters do not send the signal to the sound sensors.
10. System for processing a sound signal according to any one of claims 8 to 9, in which the geometry of the loudspeakers is positioned on an axis perpendicular to the plane of the sound sensors.
11. System for processing a sound signal according to either one of claims 8 to 9, in which the sound sensors are placed on hyperbolae situated in vertical planes.

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