HK1141149B - Method and apparatus for processing real-valued time domain signal - Google Patents

Description

Method and apparatus for processing real-valued time-domain signals

This application is a divisional application of the invention patent application having application number 02806796.7, filed on 3/28/2002, entitled "aliasing reduction with complex-exponential modulated filterbank".

Technical Field

The present invention relates to the field of subsampled digital filterbanks and provides a method and apparatus for substantially reducing the loss arising from modifying, e.g. quantizing or attenuating, the spectral coefficients or subband signals of a digital filterbank. The invention can be applied to digital equalizer (high-efficiency 20-band digital audio equalizer A.J.S.Ferreira, J.M.N.Viera, AES preprint, 98)^thConvention 1995 February 25-28Paris, n.y., USA), an adaptive filter [ (subband adaptive filtering with critical sampling: analysis, experimentation and application to echo cancellation "a. gilloid, m.vetterli, IEEE Transactions on Signal Processing, vol.40, No.8, August, 1992 ], multiband Signal companders, and audio coding systems using High Frequency Reproduction (HFR), in which digital filter banks are used for adaptive adjustment of spectral envelopes, such as Spectral Band Replication (SBR) systems [ WO98/57436 ].

Background

A digital filter bank is a collection of two or more parallel digital filters. The analysis filterbank divides the input signal into a plurality of independent signals, called subband signals (or spectral coefficients). The filter bank is critically sampled (or highest sampled) when the total number of samples per unit time subband is the same as the total number of samples of the input signal. The synthesis filter bank combines these subband signals into an output signal. One popular type of critically sampled filter bank is the cosine modulated filter bank. In cosine modulated systems the filter is obtained by cosine modulating a low pass filter, a so-called prototype filter. The cosine modulator bank provides a very efficient implementation and is often used in natural speech codecs [ (introduction to perceptual coding "K. Brandenburg, AES, Collected Papers on Digital Audio bit Reduction, 1996 ]. However, any attempt to modify the subband samples or spectral coefficients by applying an equalizing gain curve or quantized samples results in the presence of severe aliasing artifacts in the output signal.

Disclosure of Invention

The invention shows that the impairment arising from the modified subband signals can be greatly reduced by expanding the cosine modulated filter bank with the imaginary sine modulated part to form a complex index modulated filter bank. The sine extension eliminates the dominant aliasing term present in the cosine modulated filter bank. In addition, the present invention provides a method for optimizing a prototype filter, referred to as Aliasing Term Minimization (ATM). Complex exponential modulation produces complex-valued subband signals that can be interpreted as analytic signals of the signal obtained from the real part of the filter bank, i.e. the underlying cosine modulated filter bank. This function provides an inherent measure of the instantaneous energy of the subband signals.

The main steps of the operation of the complex-exponential modulated filter bank according to the invention are:

1. designing a symmetric low pass filter with a cut-off frequency of pi/2M that is optimized for desired aliasing suppression and pass band flatness;

2. forming an M-channel filter bank by complex exponential modulation of the optimized prototype filter;

3. filtering the real-valued time-domain signal through an analysis portion of a filter bank;

4. modifying the complex-valued subband signals according to a desired, possibly time-varying, equalizer setting;

5. filtering the modified complex-valued subband samples through a synthesis portion of a filter bank; and

6. the real part of the complex-valued time-domain output signal obtained from the synthesis part of the filter bank is calculated.

According to the invention, there is provided a method for estimating an energy measure of coefficients or subband signals obtained from a digital filter bank, characterized by: optimizing the filter order to N, without forcing a symmetrical low-pass prototype filter p with full reproduction₀(n); creating an analysis filter bank of M channels by complex-exponential modulating the prototype filter, wherein the filter bank has the following filter coefficients:

and N-0, 1, N, M-1; filtering a real-valued time-domain signal through the filter bank; and calculating the squared absolute value of the complex-valued subband signals obtained from said filtering.

According to the present invention, there is also provided a method for reducing aliasing arising from modifying coefficients or subband signals obtained by a digital filter bank, characterized by: optimizing the filter order to N, without forcing a symmetrical low-pass prototype filter p with full reproduction₀(n); building a filter bank of M channels by complex exponential modulation of the prototype filter, whereinThe filter bank has the following analysis and synthesis filter coefficients:

n-0.. N and k-0.. M-1; filtering a real-valued time-domain signal by an analysis portion of the filter bank; modifying complex-valued subband signals obtained from said filtering; filtering the modified complex-valued subband signals by a synthesis part of the filter bank; and taking the real part of a complex-valued time-domain output signal, wherein the output signal is the sum of the signals obtained from the synthesis filtering.

According to the invention, there is also provided an apparatus for estimating an energy measure of coefficients or subband signals obtained from a digital filter bank, characterized by: symmetric low-pass prototype filter p for optimizing the filter order number N without forcing a full reproduction₀(n) the apparatus of (a); means for building an analysis filterbank for the M channels by complex-exponential modulating the prototype filter, wherein the filterbank has the following filter coefficients:

and N-0, 1, N, M-1; means for filtering a real-valued time-domain signal through the filter bank; and means for calculating the squared absolute value of the complex-valued subband signals obtained from said filtering.

According to the present invention, there is also provided an apparatus for reducing aliasing arising from modifying coefficients or subband signals obtained by a digital filter bank, characterized by: symmetric low-pass prototype filter p for optimizing the filter order number N without forcing a full reproduction₀(n) the apparatus of (a); means for creating a filter bank of M channels by complex-exponential modulating the prototype filter, wherein the filter bank has the following analysis and synthesis filter coefficients:

and N-0, 1, N, M-1; means for filtering a real-valued time-domain signal through an analysis portion of the filter bank; means for modifying complex-valued subband signals obtained from said filtering; means for filtering the modified complex-valued subband signals by a synthesis part of the filter bank; and means for taking the real part of a complex-valued time-domain output signal, wherein said output signal is the sum of signals obtained from said synthesis filtering.

According to the present invention, there is also provided a method of processing aliasing occurring in spectral coefficients or subband signals obtained from real-valued time domain signals using a digital filter bank, comprising: symmetrical low-pass prototype filter p providing a filter order N₀(n); building a filter bank of M channels by complex-exponential modulating the prototype filter, wherein the filter bank has analysis and synthesis filter coefficients based on the following equations:

n-0.. N and k-0.. M-1; filtering a real-valued time-domain signal by an analysis portion of the filter bank; modifying the complex-valued subband signals obtained from said filtering; filtering the modified complex-valued subband signals by a synthesis part of the filter bank; and taking the real part of the signal to obtain the output signal, wherein the filter order number N of the low-pass prototype filter is higher than 2M-1, where M is the number of channels in the digital filter bank, or wherein the optimizing the low-pass prototype filter is performed by minimizing the following complex objective function ε_tot(a) The realization method comprises the following steps:

ε_tot(a)＝aε_t+(1-a)ε_a

where a is a weighting constant, ε_tIs the error energy of the transfer function, and epsilon_aIs the total aliasing error, or wherein the analysis filterbank is used for estimating the energy measure in a high frequency reproduction system, or wherein the M-channel filterbank is used as an envelope adjustment filterbank in a high frequency reproduction system.

According to the present invention, there is also provided an apparatus for processing a real-valued time-domain signal using a digital filter bank, comprising: symmetrical low-pass prototype filter p for providing a filter order number N₀(n) the apparatus of (a); for modulation by complex exponentialsMeans for building a filter bank of M channels with analysis and synthesis filter coefficients based on the following equations:

n-0.. N and k-0.. M-1; means for filtering a real-valued time-domain signal through an analysis portion of the filter bank; means for modifying complex-valued subband signals obtained from said filtering; means for filtering the modified complex-valued subband signals and taking the real part of the signals by the synthesis part of the filter bank to obtain an output signal, wherein the filter order N of the low-pass prototype filter is higher than 2M-1, where M is the number of channels in the digital filter bank, or wherein the optimization of the low-pass prototype filter is performed by minimizing the following complex objective function ε_tot(a) The realization method comprises the following steps:

ε_tot(a)＝aε_t+(1-a)ε_a

wherein a is a weightConstant, epsilon_tIs the error energy of the transfer function, and epsilon_aIs the total aliasing error, or wherein the analysis filterbank is used for estimating the energy measure in the high frequency reproduction system, or wherein the analysis filterbank is used as an envelope adjustment filterbank in the high frequency reproduction system.

The most attractive application of the present invention is to improve various digital equalizers, adaptive filters, multiband companders and adaptive envelope adjusting filter banks for HFR systems.

Drawings

The invention will now be described, by way of example and not limitation, with reference to the accompanying drawings, in which:

FIG. 1 illustrates the analysis and synthesis portion of a digital filter bank;

FIG. 2 is a size of a complex aliasing component matrix of a cosine modulated filterbank;

FIG. 3 is a size of a complex aliasing component matrix of a complex-exponential modulated filterbank;

FIG. 4 illustrates the desired terms and the main aliasing terms in a cosine modulated filter bank adjusted for the band pass filter response;

FIG. 5 illustrates the attenuation of aliasing gain terms for different implementations of a complex-exponential modulated filterbank;

FIG. 6 illustrates an analysis portion of a complex-exponential modulated filter bank system according to the present invention; and

fig. 7 illustrates the synthesis portion of a complex-exponential modulated filter bank system according to the present invention.

Detailed Description

It should be understood that the present invention is applicable to a range of implementations incorporating digital filter banks other than those explicitly mentioned in this patent.

Digital filter bank

The digital filter bank is a collection of two or more parallel digital filters sharing a common input or common output ("multirate system and filter bank" p.p.vaidyanatonneprefix Hall: englewood Cliffs, NJ, 1993 ]. When the common input is common, the filter bank is referred to as an analysis filter bank. The analysis group divides the input signal into M independent signals called subband signals. The analysis filter is denoted as H_k(z), wherein k is 0. The analysis filter is critically sampled (or most highly sampled) when the subband signal has a sampling factor of M. The total number of sub-band samples per unit time is equal to the number of samples per unit time of the input signal. The combining group combines these subband signals into a common output signal. The synthesis filter is denoted F_k(z), wherein k is 0. Fig. 1 illustrates a highest-sampling filter bank with M channels (subbands). The analyzing section 101 generates a signal V_k(z) which constitutes a signal transmitted, stored or corrected from the input signal x (z). The synthesizing section 102 recombines the signal V_k(z) is the output signal

Recombination of V_k(z) to obtain an approximation of the original signal X (z)Multiple errors are prone to occur. One of the errors is aliasing, which is caused by sampling and inserting subbands. Other errors are phase and amplitude distortions.

Analysis of the filter H according to the symbolic representation of FIG. 1_kThe output of (z)103 is:

X_k(z)＝H_k(z)X(z) (1)

m-1, where k is 0. The sampler 104 gives the following outputs:

wherein W is e^-i2π/M. InterposerThe output of 105 is given by the following equation:

and the sum of the signals obtained from the synthesis filter 106 can be written as:

wherein

Is the ith alias term X (zW)^l) The gain of (c). Equation (4) can be written as:

the final sum of the Right Hand Side (RHS) constitutes the sum of all unwanted aliasing terms. Eliminating all aliasing, i.e. by choosing H correctly_k(z) and F_k(z) making this sum 0, the following formula is given:

wherein

Is the overall transfer function or distortion function. Selecting a synthesis filter F_k(z) to

F_k(z)＝z^-NH_k(z) (9)

Where N is the number of stages of the analysis filter, resulting in the following transfer function:

the symbol H (z) is the sequence h of time reversal and complex convolution_k(n) Z-transform. Equation (10) is evaluated on a unit circle to yield:

equation (11) indicates that t (z) has a linear phase and thus no phase distortion. Furthermore, if the last sum on RHS is constant, there is no amplitude distortion. The total transfer function is in this case only a delay with a constant scaling factor c, i.e.:

T(z)＝cz^-N (12)

substituting it into equation (7) yields:

the type of filter satisfying equation (13) is referred to as having a full reproduction (PR) characteristic.

Cosine modulated filter bank

In a cosine modulated filter bank, an analysis filter h_k(n) is a symmetrical low-pass prototype filter p₀Cosine modulation model of (n):

where M is the number of channels, k is 0.. M-1, N is the prototype filter order, and N is 0.. N. The sum of the real-valued prototype filter coefficients is assumed to be 1:

with the same sign, the synthesis filter is given by the following equation:

the analysis filter bank generates real-valued subband samples for a real-valued input signal. The sub-band samples are downsampled by a factor of M, which causes the system to be critically sampled. Depending on the choice of the prototype filter, the filter bank may constitute a nearly complete reproduction system, a so-called pseudo-QMF bank [ US5436940 ], or a complete reproduction (PR) system. An example of a PR system is the Modulated Lapped Transform (MLT) ("lapped transform for efficient transform/subband coding" H.S.Malvar, IEEE Trans ASSP, vol.38, No.6, 1990). One inherent characteristic of selective modulation is that each filter has two passbands; one in the positive frequency range and one corresponding passband in the negative frequency range.

Equation (5) is written in matrix form as:

a＝Hf (17)

or specifically:

the matrix H is called an Aliasing Component (AC) matrix. To better analyze this formula, f can be written as:

or compressed as:

f＝Fe (20)

substituting equation (20) into equation (17), the aliasing gain can be written as a-HFe, where the product is

HF＝U (21)

Is an M x M matrix and is referred to herein as a composite aliasing component matrix.

For cosine modulation systems, the most important terms in the complex aliasing component matrix are the first row and the four diagonals. The three-dimensional diagram of fig. 2 illustrates the size of the individual components in this matrix. The first row holds the term from the transfer function, equation (8), while the four diagonals mainly include the dominant aliasing term, i.e., the aliasing due to the overlap between the filters and their nearest neighbors. It is readily seen that the dominant aliasing term occurs from the frequency overlap between the positive passband of the filter in the form of frequency modulation with a positive passband, or, conversely, the negative passband of the filter in the form of frequency modulation with a negative passband. And accumulating the items of each row in the composite aliasing component matrix, namely calculating the aliasing gain, and eliminating the main aliasing item as a result. Aliasing is cancelled in a pairwise manner, where a first primary aliasing term is cancelled by a second primary aliasing term in the same row. Superimposed on the primary alias term is the other smaller alias term. These aliasing terms will be large if the characteristics of the prototype filter are such that the transition and stop bands of the filter overlap with their modulation models by a large amount. For example, the second and last rows include aliasing terms due to filters overlapping with their nearest modulation models. For PR systems, these smaller aliasing terms are also completely eliminated when adding the terms to the aliasing gain. However, in the pseudo-QMF system, these terms still exist.

Complex exponential modulated filter bank

Expanding cosine modulation to complex exponential modulation according to the invention yields the following analysis filter h_k(n)：

With the same sign as before, this can be seen as adding an imaginary part to the real-valued filter bank, where the imaginary part consists of the sinusoidal modulation model of the same prototype filter. Considering an input signal of real values, the output from the filter bank can be interpreted as a set of subband signals, where the real and imaginary parts are Hilbert (Hilbert) transforms of each other. The resulting subband is thus an analysis signal of the real-valued output obtained from the cosine modulated filter bank. Therefore, the subband signal oversampling (oversampling) coefficient is 2, since it is represented by a complex value.

The synthesis filter is extended in the same way as follows:

equations (22) and (23) imply that the output from the synthesis set is complex-valued. Using matrix symbols, where C_aIs a matrix with an analysis filter from equation (14), and S_aIs a matrix with the following filters:

the filter of equation (22) is obtained as C_a+jS_a. In these matrices, k is the row index and n is the column index. Similarly, matrix C_sWith a synthesis filter from equation (16), and S_sIs a matrix with the following filters.

Equation (23) can therefore be written as C_s+jS_sWhere k is the column index and n is the row index. To represent the input signal x, the output signal y is found from the following equation:

y＝(C_s+jS_s)(C_a+jS_a)x＝(C_sC_a-S_sS_a)x+j(C_sS_a+S_sC_a)x (26)

as can be seen from equation (26), the real part includes two terms: the output from a normal cosine modulated filter bank and the output from a sine modulated filter bank. It is easy to verify that if the cosine modulated filter bank has PR characteristics, its sine modulation model, after changing sign, also constitutes a PR system. Thus, by taking the real part of the output, the complex exponential modulation system provides the same reproduction accuracy as the corresponding cosine modulation model.

The complex exponential modulation system can be extended to also handle complex valued input signals. By expanding the number of channels to 2M, i.e. increasing the negative frequency of the filter and keeping the imaginary part of the output signal, a pseudo-QMF or PR system for complex valued signals can be obtained.

The complex aliasing component matrix from equation (21) is analyzed and the main aliasing diagonal becomes zero for the complex exponential modulated filter bank. This is easily understood because the complex-exponential-modulation filter bank has only one passband per filter. In other words, the filter bank has no primary aliasing term and does not rely on the above-described pairwise aliasing cancellation. The composite aliased component matrix has only important terms in the first row. Fig. 3 shows the size of the components in the resulting matrix. The terms of row 1 through row M-1 are more or less attenuated depending on the characteristics of the prototype filter. The absence of the main aliasing term makes aliasing cancellation constrained by the discarded cosine (or sine) modulated filterbank in the complex-exponential modulation model. Thus both analysis and synthesis filters can be found from:

since for a symmetric prototype filter, p₀(n)＝p₀(N-N). As before, M is the number of channels, k is 0.. M-1, N is the prototype filter order, and N is 0.. N.

Referring to equation (4), the signal is outputZ transform of real part of (2):

symbolIs a complex convolution sequenceZ transformation of (1). From equation (4), the transformation of the real part of the output signal is:

where the input signal x (n) is typically a real number. Equation (29) can be written as:

by examining equation (30), and recalling the transformation of equation (28), it is apparent that a₀The real part of (n) must be a dirac pulse to the PR system. In addition, a_M/2The real part of (n) must be 0 and the aliasing gain, l 1.. M/2-1, must satisfy:

A_M-l(z)＝-A_l*(z) (31)

in the pseudo-QMF system, equation (31) only approximately applies. In addition, a₀The real part of (n) is not completely a dirac pulse, a_M/2The real part of (n) is not completely 0.

Modifying subband signals

Changing the gain of the channels in the cosine modulated filterbank, i.e. using the analysis/synthesis system as an equalizer, results in severe distortion due to the main aliasing term. Let us assume that our purpose is to adapt an eight-channel filter bank for a band-pass response, where all subband signals except the second and third channel are set to 0. The composite aliasing component matrix from equation (21) is then an 8 x 8 matrix in which all elements except the elements of the second and third columns are 0 (fig. 4). As shown, 7 large aliasing terms remain. Aliasing from lines three and five will be cancelled because the dominant aliasing terms have the same gain in these lines, i.e., pair wise cancellation is intentionally arranged. However, in rows two, four and six, there is only one aliasing term because their corresponding aliasing terms have zero gain. Aliasing cancellation is therefore not intentionally arranged and the aliasing in the output signal will be large.

It is clear from this example that a great improvement can be achieved when using a complex-exponential modulated filter bank as an equalizer. The 8-channel system depicted in fig. 4 has a prototype filter of 128 stages. The total aliasing attenuation in the above equalizer example is only 16 dB. Turning to complex exponential modulation results in an aliasing attenuation of 95 dB. Since there is no primary aliasing term, the resulting aliasing depends only on the suppression of the aliasing term resulting from the overlap between the secondary filters and their modulation models. It is therefore important to design a prototype filter to maximize the rejection of the aliasing gain term. The RHS first term of equation (30) calculated on the unit circle gives the error energy e of the transfer function_tComprises the following steps:

the total aliasing energy e can be calculated by calculating all remaining terms of the RHS of equation (30) on the unit circle_aComprises the following steps:

due to symmetry, formula (9) and

P₀(z)＝z^-NP₀(z) (34)

the terms in parentheses of the summation of equation (33) are equal. The total aliased energy thus has an M/2-1 term:

(35)

minimizing the aliasing gain term is achieved by optimizing the prototype filter. This is preferably achieved by minimizing the composite objective function using standard non-linear optimization algorithms, such as the Down simple method [ "digital methods in C, second edition of computational science and technology", W.H.Press, S.A.Teukolsky, W.T.Vetterling, B.P.Flannery, Cambridge University Press, NY, 1992 ]. For Aliasing Term Minimization (ATM) of a prototype filter according to the invention, the objective function is like the following formula:

ε_tot(a)＝aε_t+(1-a)ε_a (36)

during the optimization, when calculating epsilon_aApplying a random quantization curve to the filter bank, i.e. the analysis and synthesis filters multiplied by a gain factor g_k：

And in calculating the aliasing gain term A_lWhen (z), l 1.. M-1, the obtained filter H is used_k ^(eq)And F_K ^(eq)，k＝0...M-1。

In fig. 5, the aliasing gains of five different complex exponential modulation systems are compared. Of which 4 are 8 channel systems and 1 is a 64 channel system. All of these systems have a prototype filter length of 128. The dotted lines and the solid lines with asterisks illustrate the aliasing components of two pseudo-QMF systems, one of which is minimized by the aliasing term. The dashed and dashed-dotted lines are components of two 8-channel fully-reproduced systems, one of which is also minimized by aliasing terms. The solid line is the aliasing component of the complex-exponential Modulated Lapped Transform (MLT). All of these systems were tuned for bandpass response according to the above example, with the results shown in table 1. The suppression of total aliasing can be computed as the inverse of equation (33). The pass band flatness can be calculated as the inverse of equation (32) with the integration interval adjusted for the pass band response.

TABLE 1

System for controlling a power supply	Suppression of total aliasing	Pass band flatness
			8-channel pseudo-QMF ATM N-128	114.7dB	98.1dB
8-channel pseudo-QMF N-128	95.4dB	87.6dB
			8 channel PR ATM N127	77.3dB	132.7dB
8 channel PR N127	55.0dB	93.6dB
			64 channel MLT 127	38.5dB	87.1dB

As can be seen from the numbers in Table 1, a significant improvement is achieved when moving from a 64-channel MLT to an 8-channel PR system. MLT is a full reproduction system, and each polyphase component has only (N +1)/2M ═ 1 coefficients. The coefficient number of the 8-channel PR system is 128/16-8. This results in a filter with higher stopband attenuation and higher aliasing term rejection. Furthermore, it can be seen that minimizing the aliasing term in a PR system can suppress aliasing and greatly improve pass band flatness. Comparing the pseudo-QMF system with the PR system, it is clear that the aliasing suppression is improved by 40dB while almost maintaining the band pass flatness. When the aliasing term is minimized, the aliasing is additionally suppressed by about 20dB, improving the pass band flatness by 10 dB. It is therefore clear that the full reproduction constraint imposes a limit on the filters used in the equalization system. pseudo-QMF systems can always be designed for sufficient reproduction accuracy because all practical digital implementations have only a limited resolution in the digital representation. For pseudo-QMF and PR systems, it is clear that the best system is built on a large number of prototype filters that suppress the stop band. This enhances the use of prototype filters having a relative length longer than the window used in MLT.

The great advantage of the complex exponential modulation system is that the instantaneous energy is easily calculated since the subband signals constitute the analysis signal of the real-valued subband signals obtained from the cosine modulated filter bank. This is a valuable feature in e.g. adaptive filters, Automatic Gain Control (AGC), in multi-band companders and in spectral band replication Systems (SBR), where filter banks are used for spectral envelope adjustment. The average energy within subband k may be calculated as:

wherein v is_k(n) is the subband sample for channel k, and w (n) is a window of length 2L-1 centered at n-0. This measurement can then be used as an input parameter for an adaptation or gain calculation algorithm.

Practical implementation

Real-time operation of the complex exponential modulated filter bank can be achieved using a standard PC or DSP. The filter bank may also be hard coded onto a custom chip. Fig. 6 illustrates the structure of an efficient implementation of the analysis portion of a complex-exponential modulated filter bank system. The analog input signal is first fed to an a/D converter 601. The digital time domain signal is fed into a shift register 602 which holds 2M samples at a time, shifted by M samples. The signal from the shift register is then filtered by the polyphase coefficients of the prototype filter 603. The filtered signals are then combined 604 and transformed in parallel by DCT-IV605 and DST-IV 606 transforms. The outputs from the sine and cosine transforms constitute the real and imaginary parts of the sub-band samples, respectively. The gains of the sub-band samples are modified according to the current spectral envelope adjuster setting 607.

Fig. 7 illustrates an efficient implementation of the synthesis part of a complex exponential modulation system. The sub-band samples are first multiplied by a complex exponential rotation coefficient 701, the real part is modulated with a DVT-IV 702 and the imaginary part is modulated with a DST-IV 703 transform. The outputs from the converters are combined 704 and fed through the polyphase components of the prototype filter 705. A time domain output signal is obtained from the shift register 706. Finally, the digital output signal is converted back to the analog waveform 707.

The above-described embodiments merely illustrate the principles of a complex-exponential modulated filter bank system according to the present invention. It is understood that modifications and variations of the arrangements and details described herein will be apparent to those skilled in the art. The invention is therefore limited only by the scope of the following patent claims and not by the specific details provided by the description and the explanation of the embodiments herein.

Claims (6)

1. A method of processing a real-valued time-domain signal, comprising:

symmetrical low-pass prototype filter p providing a filter order N₀(n)；

Building an M-channel digital filter bank by complex-exponential modulating the symmetric low-pass prototype filter, wherein the M-channel digital filter bank has analysis partial filter coefficients and synthesis partial filter coefficients based on the following equations:

n-0.. N and k-0.. M-1;

-filtering a real-valued time-domain signal by an analysis part (602, 603, 604, 605, 606) of said M-channel digital filter bank;

modifying complex-valued subband signals obtained from filtering real-valued time-domain signals;

-filtering said modified complex-valued subband signals by a synthesis part (702, 703, 704, 705, 706) of said M-channel digital filter bank; and

taking the real part of the signal to obtain an output signal,

wherein the symmetric low-pass prototype filter has a filter order N higher than 2M-1, where M is the number of channels in the digital filter bank of the M channels, or

Wherein optimizing the symmetric low-pass prototype filter is performed by minimizing a composite objective function ε_tot(a) The realization method comprises the following steps:

ε_tot(a)＝aε_t+(1-a)ε_a

where a is a weighting constant, ε_tIs the error energy of the transfer function, and epsilon_aIs a total mixtureOverlay error, or

Wherein the analysis portion of the M-channel digital filter bank is used to estimate an energy measure in a high frequency reproduction system, or

Wherein the M-channel digital filter bank is used as an envelope adjustment filter bank in a high frequency reproduction system.

2. The method of claim 1, wherein a gain adjustment model h of a filter of the analysis portion of the M-channel digital filter bank and a filter of the synthesis portion of the M-channel digital filter bank is utilized according to the following formula_k ^(eq)(n)，f_k ^(eq)(n) calculating the aliasing gain term:

and

wherein g is_kA real-valued gain coefficient representing randomization or certainty, N0.. N, k 0.. M-1, and wherein h_k(n)，f_k(n) digital filters each of said M channelsFilter coefficients of filters of the analysis portion of the bank and filters of the synthesis portion of the digital filter bank of the M channels.

3. A method according to any one of claims 1-2, wherein the digital filter bank of the M channels is used as a filter in a digital equalization system.

4. The method according to any of claims 1-2, wherein the M-channel digital filter bank is used in an adaptive filtering system.

5. The method according to any of claims 1-2, wherein the M-channel digital filter bank is used in a multiband compander system.

6. An apparatus for processing a real-valued time-domain signal, comprising:

symmetrical low-pass prototype filter p for providing a filter order number N₀(n) the apparatus of (a);

means for building an M-channel digital filter bank by complex-exponential modulating the symmetric low-pass prototype filter, wherein the M-channel digital filter bank has analysis partial filter coefficients and synthesis partial filter coefficients based on the following equations:

n-0.. N and k-0.. M-1;

-means for filtering a real-valued time-domain signal by an analysis part (602, 603, 604, 605, 606) of said M-channel digital filter bank;

means for modifying complex-valued subband signals obtained by said means for filtering real-valued time-domain signals;

means for filtering the modified complex-valued subband signals and taking the real part of the signal by a synthesis part (702, 703, 704, 705, 706) of said M-channel digital filter bank to obtain an output signal,

wherein the symmetric low-pass prototype filter has a filter order N higher than 2M-1, where M is the number of channels in the digital filter bank of the M channels, or

Wherein optimizing the symmetric low-pass prototype filter is performed by minimizing a composite objective function ε_tot(a) The realization method comprises the following steps:

ε_tot(a)＝aε_t+(1-a)ε_a

where a is a weighting constant, ε_tIs the error energy of the transfer function, and epsilon_aIs the total aliasing error, or

Wherein the analysis portion of the M-channel digital filter bank is used to estimate an energy measure in a high frequency reproduction system, or

Wherein the M-channel digital filter bank is used as an envelope adjustment filter bank in a high frequency reproduction system.