ES2748579T3 - Low delay modulated filter bank - Google Patents

Abstract

A signal processing device for filtering and performing high frequency reconstruction of an audio signal, wherein the signal processing device comprises: a bank of analysis filters that receives real-value time domain input audio samples and generates complex value subband samples; a unit that generates modified complex value subband samples by modifying gains of complex value subband samples according to the current setting of the spectral envelope adjuster; and a synthesis filter bank that receives the modified complex value subband samples and generates time domain output audio samples, wherein the synthesis filter bank comprises M synthesis filters fk (n) that are versions modulated by Complex exponential of a prototype filter p0 (n) according to: where the bank of analysis filters comprises K analysis filters, with K different from M, which are versions modulated by complex exponential of a prototype filter obtained from the prototype filter p0 (n) by resampling the prototype filter p0 (n) through decimation or interpolation, where the prototype filter p0 (n) has a length N, and where the bank of analysis filters and the bank of synthesis filters have a set delay of D samples.

Description

DESCRIPTION

Low delay modulated filter bank

This document relates to modulated subsampled digital filter banks, as well as methods and systems for the design of such filter banks. In particular, it provides a newly designed method and apparatus for a near-perfect reconstruction complex exponential or low-delay cosine modulated filter bank, optimized for aliasing or overlap suppression arising from modifications of spectral coefficients or subband signals. . In addition, a specific design is provided for a 64-channel filter bank that uses a prototype filter length of 640 coefficients and a system delay of 319 samples.

The guidance in this document may apply to digital equalizers, as noted, p. ex. in "An Efficient 20 Band Digital Audio Equalizer" A. J. S. Ferreira, J. M. N. Viera, AES prepress, 98th Convention 1995 February 25-28 Paris, N.Y., USA; adaptive filters, as noted, p. eg, in Adaptive Filtering in Subbands with Critical Sampling: Analysis, Experiments, and Application to Acoustic Echo Cancellation »A. Gilloire, M. Vetterli, IEEE Transactions on Signal Processing, vol. 40, No. 8, August 1992; multiband compressors; and to audio encoding systems that use high frequency reconstruction (HFR) methods; or audio coding systems that use so-called parametric stereo techniques. In the last two examples, a digital filter bank is used for adaptive adjustment of the spectral envelope of the audio signal. An example of an HFR system is the noted Spectral Band Replication System (SBR), e.g. eg, in WO 98/57436, and a parametric stereo system is described, eg. eg, in EP1410687. US 2007/179781 A1 describes a method for designing a complex modulated filter bank. Dumitrescu et. al, "Simplified Design of Low-Delay Oversampled NPR GDFT Filterbanks", 2005 IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 4, 18.03.2005, describes a method for designing filter banks with almost perfect reconstruction. EP 1994530 A1 describes a method of generating audio subband values.

Throughout this description including the claims, the terms "subband signals" or "subband samples" denote the output signal or output signals, or output sample or output samples of the analysis part of a test bench. digital filters or the output of a direct transform, that is, the transform that operates on data in the time domain, of a transform-based system. Examples for the output of such direct transforms are the frequency domain coefficients of a digital Fourier transform (DFT) with windows or the output samples from the analysis stage of a modified discrete cosine transform. (MDCT).

Throughout this description including the claims, the term "overlap" denotes a nonlinear distortion resulting from decimation and interpolation, possibly in combination with modification (eg, attenuation or quantification) of the subband samples in a bank of subsampled digital filters.

A digital filter bank is a set of two or more parallel digital filters. The analysis filter bank divides the incoming signal into a number of separate signals that are called subband signals or spectral coefficients. The filter bank is critically sampled or decimated to the maximum when the total number of subband samples per unit time is the same as for the input signal. A so-called synthesis filter bank combines the subband signals into an output signal. A popular type of critically sampled filter bank is the cosine modulated filter bank, where filters are obtained by cosine modulation of a low-pass filter, a so-called prototype filter. The cosine modulated filter bank offers efficient implementations and is often used in natural audio encoding systems. For further details, reference is made to "Introduction to Perceptual Coding" K. Brandenburg, AES, Collected Papers on Digital Audio Bitrate Reduction, 1996.

A common problem in filter bank design is that any attempt to alter subband samples or spectral coefficients, e.g. For example, by applying an equalization gain curve or by quantizing the samples, it typically produces overlapping defects in the output signal. Therefore, filter bank designs that reduce such defects are desirable even when subband samples undergo severe modifications.

One possible approach is the use of oversampled filter banks, that is, not critically sampled. An example of an oversampled filter bank is the complex exponential modulated filter bank class, where an imaginary sine modulated part is added to the real part of a cosine modulated filter bank. Such a complex exponential modulated filter bank is described in EP1374399.

One of the properties of complex exponential modulated filter banks is that they are free from the main alias terms present in cosine modulated filter banks. As a result, such filter banks are typically less prone to modification-induced defects in subband samples. However, other alias terms remain and sophisticated design techniques must be applied for the prototype filter of such a complex exponential modulated filter bank in order to minimize degradation, such as overlap, arising from modifications of the subband signals. Typically, the remaining alias terms are less significant than the main alias terms.

An additional property of filter banks is the amount of delay a signal incurs when it passes through these filter banks. In particular, for real-time applications, such as audio and video broadcasts, the filter or system delay should be low. A possible approach to obtain a filter bank that has a low total system delay, that is, a low delay or latency of a signal that passes through an analysis filter bank followed by a synthesis filter bank, is the use of short symmetric prototype filters. Typically the use of short prototype filters leads to relatively poor frequency band separation characteristics and large areas of frequency overlap between adjacent subbands. Consequently, short prototype filters typically do not allow for a filter bank design that adequately suppresses overlap when modifying subband samples, and other approaches to low delay filter bank design are required.

Therefore, it is desirable to provide a filter bank design method that combines a number of desirable properties. These properties are a high level of insensitivity to signal degradation, such as overlap, subject to modifications of subband signals; a low delay or latency of a signal that passes through the analysis and synthesis filter banks; and a good approximation of the perfect rebuilding property. In other words, it is desirable to provide a design method for filter banks that generates a low level of errors. Subsampled filter banks typically generate two types of errors, linear distortion of the passband term that can be further divided into phase and amplitude errors, and nonlinear distortion arising from the overlap terms. Although a "good approximation" of the PR property (perfect reconstruction) would keep all these errors at a low level, it might be beneficial from a perceptual point of view to place a greater emphasis on the reduction of distortions produced by overlap.

Also, it is desirable to provide a prototype filter that can be used to design an analysis and / or synthesis filter bank that exhibits such properties. Another desirable property of a filter bank is that it has an almost constant group delay so as to minimize defects due to phase dispersion of the output signal.

This document shows that degradation arising from subband signal modifications can be significantly reduced by employing a filter bank design method, referred to as the Enhanced Alias Term Minimization Method (IATM). in English), for the optimization of symmetric or asymmetric prototype filters.

This document indicates that the concept of pseudo QMF (Quadrature Mirror Filter) designs, i.e. near perfect rebuild filter bank designs, can be extended to cover low delay filter bank systems that they use asymmetric prototype filters. As a result, near-perfect reconstruction filter banks can be designed with low system delay, low overlap sensitivity and / or low passband error level including phase dispersion. Depending on the particular needs, the emphasis placed on any of the filter bank properties can be changed. Therefore, the filter bank design method according to the present document reduces the current limitations of PR filter banks used in an equalization system or other system that modifies the spectral coefficients.

The design of a low delay complex exponential modulated filter bank according to the present document can comprise the steps:

• a prototype asymmetric low-pass filter design with a cutoff frequency of n / 2M, optimized for desired overlap and passband error rejections, further optimized for a system D delay ; where M is the number of channels in the filter bank; Y

• a construction of an M channel filter bank using complex exponential modulation of the optimized prototype filter.

Furthermore, the operation of said low delay complex exponential modulated filter bank according to the present document may comprise the steps:

• filtering of a time domain signal with real value through the analysis part of the filter bank;

• a modification of complex value subband signals, eg. eg, according to a desired equalizer setting, possibly time-varying;

• filtering the modified complex value subband samples through the synthesis part of the filter bank; Y

• a calculation of the real part of the complex value temporal domain output signal obtained from the synthesis part of the filter bank.

In addition to introducing a new filter design method, this document describes a specific design of a 64 channel filter bank that has a prototype filter length of 640 coefficients and a system delay of 319 samples.

The indications in this document, in particular the proposed filter bank and the filter banks designed according to the proposed design method can be used in various applications. Such applications are the enhancement of various types of digital equalizers, adaptive filters, multi-band compressors, and adaptive envelope adjustment filter banks used in HFR or parametric stereo systems.

According to a first aspect, a method is described for determining N coefficients of an asymmetric prototype filter p ^o for use to construct an M- channel low delay subsampled analysis / synthesis filter bank. The analysis / synthesis filter bank can comprise M analysis filters h ^k and M synthesis filters f ^k , where k takes values from 0 to M-1 and where typically M is greater than 1. The filter bank of analysis / synthesis has a general transfer function, which is typically associated with the coefficients of the analysis and synthesis filters, as well as decimation and / or interpolation operations.

The method comprises the step of choosing a target transfer function from the filter bank comprising a target delay D. Typically a target delay D that is less than or equal to N is selected. The method further comprises the step of determining a composite target function. e ^tot comprising a passband error term e ^t and an overlap error term ea. The passband error term is associated with the deviation between the filter bank transfer function and the target transfer function, and the overlap error term e ^a is associated with errors incurred due to subsampling, i.e. decimation and / or interpolation of the filter bank. In another stage of the method, the N coefficients of the asymmetric prototype filter p ^o that reduce the composite objective function e ^{tot are determined} .

Typically, the step of determining the objective error function et ^ot and the step of determining the N asymmetric prototype filter coefficients p ^o are repeated iteratively, until a minimum of the objective error function e ^tot is reached ^. In other words, the objective function e ^tot is determined based on a given set of coefficients of the prototype filter, and an updated set of coefficients of the prototype filter is generated by reducing the objective error function. This process is repeated until further reductions in objective function can be achieved through modification of the prototype filter coefficients. This means that the step of determining the objective error function e ^tot may comprise determining a value for the composite objective function e ^tot for given coefficients of the prototype filter p ^o and the step of determining the N coefficients of the asymmetric prototype filter p ^o may comprise determining updated coefficients of the prototype filter p ^o as a function of the gradient of the composite objective function e ^tot associated with the coefficients of the prototype filter p ^o .

According to another aspect, the compound objective error function e ^tot is given by:

where e ^t is the passband error term, e ^a is the overlap error term ya is a weighting constant that takes values between 0 and 1. The passband error term e ^t can be determined by accumulating the square deviation between the filter bank transfer function and the objective transfer function for multiple frequencies. In particular, the passband error term e ^t can be calculated as

where P ( o>) e ~ jwD is the objective transfer function, and

AJ z) = Y j Hí ( z) F í ( z)

k 0

where H ^k ( z) and F ^k ( z) are the z transforms of the analysis and synthesis filters h ^k ( n) and f ^k ( n), respectively.

The overlap error term e ^a is determined by accumulating the squared magnitude of the alias gain terms for multiple frequencies. In particular, the overlap error term e ^a is calculated as

l = 1 ... M-1 , for z = j and with

^{M *) =} S ^{Hk (zWl) Fk (z)}

k = 0

which is the l-th alias gain term evaluated in the unit circle with W = e- ^{/ 2nlM} , where H ^k ( z) and F ^k ( z) are the z transforms of the analysis and synthesis filters hk ( n) and f ^k ( n), respectively. The notation A ^* ( z) is the z-transform of the complex conjugate sequence a ( n).

According to another aspect, the step of determining a value for the composite objective function e ^tot can comprise generating the analysis filters h ^k ( n) and the synthesis filters f ^k ( n) of the analysis / synthesis filter bank in Function of the prototype filter p ^o ( n) through the use of cosine modulation, sine modulation and / or complex exponential modulation. In particular, analysis and synthesis filters can be determined by using cosine modulation as

with n = 0 ... N-1, for the M analysis filters of the analysis filter bank

with n = 0 ... N-1, for the M synthesis filters of the synthesis filter bank;

Analysis and synthesis filters can also be determined by using complex exponential modulation such as

hk {n) = /? 0 («) exp <¡i 71 ( k ^) ( n ~ ^ ~ A)

M 2 2

with n = 0 ... N-1, and where A is an arbitrary constant, for the M analysis filters of the analysis filter bank and;

with n = 0 ... N-1, for the M synthesis filters of the synthesis filter bank;

According to another aspect, the step of determining a value for the composite objective function e ^tot may comprise setting at least one of the filter bank channels to zero. This can be achieved by applying zero gain to at least one analysis and / or synthesis filter, that is, the filter coefficients h ^k and / or f ^k can be set to zero for at least one channel k. In one example, a predetermined amount of the low frequency channels and / or a predetermined amount of the high frequency channels can be set to zero. In other words, the low frequency filter bank channels k = 0 to C ^ow ; with C ^ow greater than zero they can be set to zero. Alternatively or additionally, the high frequency filter bank channels k = C ^htgh up to M-1, with C ^htgh less than M-1 can be set to zero.

In such a case, the step of determining a value for the complex objective function e ^tot may comprise generating the analysis and synthesis filters for the overlap terms Clow and MC ^low and / or C ^h t ^gh and MC ^hgh by using modulation by complex exponential. You can further understand generating the analysis and synthesis filters for the rest of the overlap terms by using cosine modulation. In other words, the optimization procedure can be performed in a partially complex value manner, where the overlap error terms that are free from the main overlap are calculated by using actual value filters, eg. eg, filters generated through the use of cosine modulation and where the overlap error terms that carry the main overlap in a real value system are modified for complex value processing, eg. eg, through the use of complex exponential modulated filters.

According to another aspect, the analysis filter bank can generate M subband signals from an input signal using the M analysis filters h ^k . These M subband signals can be decimated by an M factor , which produces decimated subband signals. Typically, the decimated subband signals are modified, eg. eg, for equalization or compression purposes. Possibly modified decimated subband signals can be up-sampled by an M factor and the synthesis filter bank can generate a signal output from the decimated subband signals sampled upward using the M synthesis filters f ^k.

According to another aspect, an asymmetric prototype filter p ^o ( n) is described that includes coefficients that can be derived from the coefficients of Table 1 by any of the rounding, truncation, scaling, subsampling or oversampling operations. Any combination of rounding, truncation, scaling, subsampling, or oversampling is possible.

The rounding operation of the filter coefficients can comprise any of the following: rounding to more than 20 significant figures, more than 19 significant figures, more than 18 significant figures, more than 17 significant figures, more than 16 significant figures, more than 15 significant figures, more than 14 significant figures, more than 13 significant figures, more than 12 significant figures, more than 11 significant figures, more than 10 significant figures, more than 9 significant figures, more than 8 significant figures, more than 7 figures significant, more than 6 significant figures, more than 5 significant figures, more than 4 significant figures, more than 3 significant figures, more than 2 significant figures, more than 1 significant figure, 1 significant figure.

The truncation operation of the filter coefficients can comprise any of the following: truncation to more than 20 significant figures, more than 19 significant figures, more than 18 significant figures, more than 17 significant figures, more than 16 significant figures, more than 15 significant figures, more than 14 significant figures, more than 13 significant figures, more than 12 significant figures, more than 11 significant figures, more than 10 significant figures, more than 9 significant figures, more than 8 significant figures, more than 7 figures significant, more than 6 significant figures, more than 5 significant figures, more than 4 significant figures, more than 3 significant figures, more than 2 significant figures, more than 1 significant figure, 1 significant figure.

The filter coefficient scaling operation may comprise scaling up or scaling down the filter coefficients. In particular, it can comprise up and / or down scaling by the number M of filter bank channels. Such up or down scaling can be used to maintain the input power of an input signal to the filter bank at the output of the filter bank.

The subsampling operation may comprise subsampling by a factor less than or equal to 2, less than or equal to 3, less than or equal to 4, less than or equal to 8, less than or equal to 16, less than or equal to 32, less than or equal to 64, less than or equal to 128, less than or equal to 256. The subsampling operation may further include determining the subsampled filter coefficients as the mean value of the adjacent filter coefficient. In particular, the mean value of R adjacent filter coefficients can be determined as the subsampled filter coefficient, where R is the subsampling factor.

The oversampling operation may comprise oversampling by a factor less than or equal to 2, less than or equal to 3, less than or equal to 4, less than or equal to 5, less than or equal to 6, less than or equal to 7, less than or equal to 8, less than or equal to 9, less than or equal to 10. The oversampling operation may further comprise determining the oversampled filter coefficients as the interpolation between two adjacent filter coefficients.

According to another aspect, a filter bank comprising M filters is described. The filters in this filter bank are based on the asymmetric prototype filters described herein and / or the asymmetric prototype filters determined by the methods outlined herein. In particular, the M filters can be a modulated version of the prototype filter and the modulation can be a cosine modulation, a sine modulation and / or complex exponential modulation.

According to another aspect, a method is described for generating decimated subband signals with low sensitivity to overlap that arises from the modifications of said subband signals. The method comprises the steps of determining analysis filters from an analysis / synthesis filter bank according to methods outlined herein; filtering an actual value time domain signal through said analysis filters, to obtain complex value subband signals; and decimate such subband signals. Also described is a method of generating a true value output signal from multiple complex value subband signals with low sensitivity to overlap arising from modifications to such subband signals. The method comprises the steps of determining synthesis filters from an analysis / synthesis filter bank according to the methods outlined herein; interpolate said multiple complex value subband signals; filtering said multiple complex value subband signals through said synthesis filters; generate a complex value temporal domain output signal as the sum of the signals obtained from said filtering; and taking the real part of the complex value time domain output signal as the real value output signal.

According to another aspect, an operating system for generating subband signals from a temporal domain input signal is described, where the system comprises a bank of analysis filters that has been generated according to the methods indicated in this document and / or that it is based on the prototype filters indicated in this document.

It should be noted that aspects of the methods and systems, including their preferred embodiments, as outlined in this patent application can be used independently or in combination with the other aspects of the methods and systems described herein. Likewise, all aspects of the methods and systems indicated in this patent application can be combined in an arbitrary way. In particular, the features of the claims can be arbitrarily combined with each other.

The present invention will now be described by way of illustrative, non-limiting examples, with reference to the accompanying drawings, in which:

Figure 1 illustrates the analysis and synthesis sections of a digital filter bank;

Figure 2 shows stylized frequency responses for a set of filters to illustrate the adverse effect of modifying the subband samples in cosine modulated filter bank, ie, with actual value;

Figure 3 shows a flow diagram of an example of the optimization procedure;

Figure 4 shows a time domain graph and frequency response of a prototype filter optimized for a low delay modulated filter bank having 64 channels and a total system delay of 319 samples; Y

Figure 5 illustrates an example of the analysis and synthesis parts of a low delay complex exponential modulated filter bank system.

It should be understood that the present indications are applicable to a range of implementations incorporating digital filter banks other than those explicitly mentioned in this patent. In particular, the indications herein may be applicable to other methods of designing a filter bank based on a prototype filter.

The general transfer function of an analysis / synthesis filter bank is then determined. In other words, the mathematical representation of a signal that passes through said filter bank system is described. A digital filter bank is a set of M, in which M are two or more, parallel digital filters that share a common input or a common output. For details of such filter banks, reference is made to "Multirate Systems and Filter Banks" PP Vaidyanathan Prentice Hall: Englewood Cliffs, NJ, 1993. When you share a common input the filter bank can be called a test bank. The analysis bank divides the incoming signal into M separate signals which are called subband signals. The analysis filters are denoted H ^k ( z), where k = 0, ..., M-1. The filter bank is critically sampled or decimated to the maximum when the subband signals are decimated by a factor M. Therefore, the total number of subband samples per unit time in all subbands is the same as the number of samples per unit of time for the input signal. The synthesis bank combines these subband signals into a common output signal. The synthesis filters are denoted F ^k ( z), for k = 0, ..., M-1.

A maximum decimated filter bank with M channels or subbands is shown in Figure 1. Analysis part 101 produces from the input signal X (z) the subband signals V ^k ( z), which constitute the signals to be transmitted, stored or modified. Synthesis part 102 recombines signals Vk (z) to output signal X (z).

Recombination of Vk (z) to obtain the approximation X (z) of the original signal X (z) is subject to many possible errors. The errors may be due to an approximation of the perfect reconstruction property, and includes non-linear degradation due to overlap, which can be caused by decimating and interpolating the subbands. Other errors resulting from approximations of the perfect reconstruction property may be due to linear degradation such as amplitude and phase distortion.

Following the notations in Figure 1, the outputs of the analysis filters H ^k ( z) 103 are

X k ( z) = H k ( z) X ( z), (1)

where k = 0, ..., M-1. The decimators 104, also referred to as descending sampling units, give the outputs

where W = e'l2wlM. The outputs of the interpolators 105, also referred to as ascending sampling units, are given by

M - l

Uk ( z) -Vk {zM) - y - £ Hk ( zWl) X {zWl), ^(. 3 ⁾

M 1 = 0

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

where

is the gain for the / -th alias term X ( zW). Eq. (4) shows that ^ is a sum of M components consisting of the product of the modulated input signal X ( zW) and the corresponding alias gain term A ( z). Eq. (4) can be rewritten as:

The last right side sum (RHS) is the sum of all unwanted alias terms. Canceling all overlap, that is, forcing this sum to zero by using suitable choices of H ^k ( z) and F ^k ( z), gives

where

₁ M -1

7 '(z) = 77 Z Hk ( .z) Fk {z) (.8)

M k = 0

it is the general transfer function or distortion function. Eq. (8) shows that, depending on H ^k ( z) and F ^k ( z), T ( z) could be free of both phase distortion and amplitude distortion. In this case the general transfer function would simply be a delay of D samples with a constant scaling factor c, i.e.

which substituted in Eq. (7) gives

X ( z) = cz-DX ( z). ^(. 10 ⁾

Filter types satisfying Eq. (10) are said to have the perfect rebuild property (PR). If Eq. (10) is not perfectly satisfied, even if approximately satisfied, the filters are of the approximate perfect reconstruction filter class.

Next, we describe a method to design analysis and synthesis filter banks from a prototype filter. The resulting filter banks are referred to as cosine modulated filter banks. In the traditional theory of cosine modulated filter banks, the analysis filters h ^k ( n) and synthesis filters f ^k ( n) are cosine modulated versions of a prototype symmetric low pass filter p ^o ( n), it is say,

you

hk ( ti) = y¡2po ( n) cosí ■ 77 (ifc 0 <n <N, 0 <k <M 01)

I M

0 <n <N , 0 < k <M (12) respectivamente, donde M es la cantidad de canales del banco de filtros y N es el orden de filtro prototipo. fk («) = J ip or (») eos

0 <n <N, 0 <k <M (12) respectively, where M is the number of channels in the filter bank and N is the prototype filter order.

The above cosine modulated analysis filterbank produces actual value subband samples for actual value input signals. Subband samples are down-sampled by a factor M, which causes the system to be critically sampled. Depending on the choice of the prototype filter, the filter bank may constitute an approximate perfect reconstruction system, that is, a so-called described pseudo QMF bank, e.g. eg, in US5436940, or a perfect reconstruction system (PR). An example of a PR system is the Modulated Overlap Transform (MLT) described in more detail in "Lapped Transforms for Efficient Transform / Subband Coding" HS Malvar, IEEE Trans to Ss P, vol. 38, No. 6, 1990. The general delay, or system delay, for a traditional cosine modulated filter bank is N.

In order to obtain filter bank systems that have lower system delays, the present document indicates to replace the symmetric prototype filters used in conventional filter banks by asymmetric prototype filters. In the prior art, the design of asymmetric prototype filters has been restricted to systems that have the perfect reconstruction (PR) property. Such a perfect reconstruction system using asymmetric prototype filters is described in EP0874458. However, the perfect reconstitution constraint imposes limitations on a used filter bank, eg. eg, in an equalization system, due to restricted degrees of freedom when designing the prototype filter. It should be noted that symmetric prototype filters have a linear phase, that is, they have a constant group delay throughout all frequencies. On the other hand, asymmetric filters typically have a nonlinear phase, that is, they have a group delay that can change with frequency.

In filter bank systems using asymmetric prototype filters, analysis and synthesis filters can be written as

^ (fl) = ^ (») cosj ^ (* ^) (» - yy) J, 0 <n <N l :, 0 <k <M (13)

0 < n< Ny,0<k < M (14) / * (») => / 2/0 («) eos

0 < n <Ny, 0 <k <M (14)

respectively, where ha ( n) and f0 ( n) are the prototype analysis and synthesis filters of lengths Nh and Nf, respectively, and D is the total delay of the filter bank system. Without limiting the scope, the modulated filter banks studied below are systems in which the analysis and synthesis prototypes are identical, that is,

, / «(«) = * «(«) = Po ( *) , 0 <n <N i = N, - A '(15)

where N is the length of the prototype filter po ( n).

It should be noted, however, when using the filter design schemes outlined in this document, that filter banks can be determined using different prototype analysis and synthesis filters.

An inherent property of cosine modulation is that each filter has two passbands; one in the positive frequency range and a corresponding passband in the negative frequency range. It can be verified that the so-called main or significant alias terms arise from the frequency overlap between the negative pass bands of the filters with frequency modulated versions of the positive pass bands or, conversely, the positive pass bands of the filters. Filters with frequency modulated versions of the negative passbands. The last terms of Eq. (13) and (14), that is, the terms

they are selected to provide override of the main alias terms in cosine modulated filter banks. However, by modifying the subband samples, the cancellation of the main alias terms is affected, which results in a strong overlapping impact of the main alias terms. Therefore it is desirable to remove these main alias terms from the subband samples entirely.

The removal of the main alias terms can be accomplished by using so-called complex exponential modulated filter banks that are based on an extension of cosine modulation to complex exponential modulation. This extension produces the analysis filters h ^k ( n) as

h, ( n) = tt. (ji) expJ / - ( k + -) («- - T -) t, 0 < n <N, 0 < k < M (16)

'l M 2 2 2

By using the same notation above. This can be seen as adding an imaginary part to the real value filter bank, where the imaginary part consists of sine-modulated versions of the same prototype filter. Considering an input signal of real value, the output of the filter bank can be interpreted as a set of subband signals, where the real and imaginary parts are Hilbert transforms of each other. The resulting subbands are therefore the analytical signals of the actual value output obtained from the cosine modulated filter bank. Therefore, due to complex value representation, the subband signals are oversampled by a factor of two.

The synthesis filters extend in the same way to

Eqs. (16) and (17) imply that the output of the synthesis bank has a complex value. By using matrix notation, where C a is a matrix with the cosine modulated analysis filters of Eq. (13), and S a is a matrix with sine modulation of the same argument, the filters of Eq. . (16) are obtained as C a j S a. In these matrices, k is the row index and n is the column index. Analogously, matrix C s has synthesis filters from Eq. (14), and S s is the corresponding sine modulated version. Eq. (17) can therefore be written as C s j S s, where k is the column index and n is the row index. When denoting the input signal x , the output signal y is found from

y = (Cs i Ss) (Ca j Sa) x = (C, Ca - SsSa) x j (CsSa t SsCa) x (18)

As seen in Eq. (18), the real part comprises two terms; the output of the cosine modulated filter bank and an output of a sine modulated filter bank. It is easily verified that if a cosine modulated filter bank has the PR property, then its sine modulated version, with a change of sign, also constitutes a Pr system. Therefore, when taking the real part of the output, the complex exponential modulated system offers the same reconstruction precision as the corresponding cosine modulated version. In other words, by using an actual value input signal, the output signal of the complex exponential modulated system can be determined by taking the actual part of the output signal.

The complex exponential modulated system can be extended to handle complex value input signals as well. By extending the number of channels to 2M, that is, adding the filters for negative frequencies, and keeping the imaginary part of the output signal, you get a pseudo QMF or a PR system for signals of complex value.

Note that the complex exponential modulated filter bank has only one passband for each filter in the positive frequency range. Therefore, it is free from the main alias terms. The absence of major alias terms makes the cosine (or sine) modulated filterbank overlap cancellation constraint obsolete in the complex exponential modulated version. Analysis and synthesis filters, therefore, can be given as

Y

/ * («) = Fl, (fl) exp {i ^ (A - ^) (jj - ^ / <) ^ 0 <n <N, 0 <k <M (20)

_{M 2 2}

where A is an arbitrary constant (possibly zero) and, as before, M is the number of channels, N is the prototype filter length, and D is the system delay. By using different values of A, more efficient implementations of the analysis and synthesis filter banks can be obtained, that is, implementations with reduced complexity.

Before presenting a method for prototype filter optimization, the approaches to filter bank design described are summarized. Depending on symmetric or asymmetric prototype filters, filter banks can be generated, eg. For example, by modulating the prototype filters by using a cosine function or a complex exponential function. The prototype filters for the analysis and synthesis filter banks can be different or identical. When using complex exponential modulation, the main alias terms of the filter banks are deprecated and can be removed, thereby reducing the sensitivity of the overlap to modifications of the subband signals of the resulting filter banks. Furthermore, when using asymmetric prototype filters the overall system delay of the filter banks can be reduced. It has also been shown that when complex exponential modulated filter banks are used, the output signal can be determined from an actual value input signal by taking the actual part of the complex output signal from the filter bank.

A method for optimizing prototype filters is described in detail below. Depending on needs, optimization can be directed to increasing the degree of perfect reconstruction, i.e. reducing the combination of overlap and amplitude distortion, reducing sensitivity to overlap, reducing system delay, reducing distortion of phase and / or to reduce amplitude distortion. In order to optimize the prototype filter po ( n) , first expressions are determined for the alias gain terms. Next, the alias gain terms are derived for a complex exponential modulated filter bank. However, it should be noted that the alias gain terms indicated are also valid for a cosine modulated filter bank (of real value).

With reference to Eq. (4), the z-transform of the real part of the output signal x (n) is

Z ¡Re (í («))} - XR ( z) ~ Í (Z) + 2Í * (Z). ^{(twenty-one )}

The notation X * (z) is the z-transform of the complex conjugate sequence X (n). From Eq. (4), it follows that the transform of the real part of the output signal is

where it was used that the input signal x ( n) has a real value, that is, X * ( zW) = X ( zW). After reordering Eq. (22) can be written as

where

are the alias earning terms used in optimization. It can be seen from Eq. (24) that

Specifically, for real value systems

% _ / * (z) = 4 (2) (26)

which simplifies Eq. (24) in

A / ( z) = A} ( z), ( ) </ <M. (27)

By inspecting Eq. (23), and taking into account the transform of Eq. (21), it can be seen that the real part of a0 ( n) must be a Dirac impulse for a PR system, i.e.Ao ( z) is in the form Ao ( z) = czD. On the other hand, the real part of aw / 2 (n) must be zero, that is, Á mh ( z) must be zero and the alias earnings, for 11 0, M / 2 must satisfy

Am - i ( z) = -A / * ( z) , (28)

which for a real value system, with Eq. (26) in mind, means that all ai ( n), l = 1 ... M-1 must be zero. In pseudo QMF systems, Eq. (28) is valid only approximately. On the other hand, the real part of ao ( n) is not exactly a Dirac pulse, nor is the real part of aw / 2 (n) exactly zero.

Before going into further detail on optimizing prototype filters, we investigate the impact of subband sample modifications on overlap. As already mentioned above, changing the Channel gains in a cosine modulated filter bank, that is, using the analysis / synthesis system as an equalizer, produces severe distortions due to the main alias terms. In theory, the main alias terms cancel each other in pairs. However, this principal aliasing term cancellation theory is not satisfied when different gains are applied to different subband channels. Therefore, the overlap in the output signal can be substantial. To show this, consider a filter bank in which the p- channel and the highest channels are set to zero gain, i.e.

{ah ~ 1, 0 <k <p

ñ í n) - u v * (»), (29)

U a- = ° , p <k <M - 1

The stylized frequency responses of the analysis and synthesis filters of interest are shown in Figure 2. Figure 2 (a) shows the synthesis channel filters Fp-1 ( z) and Fp ( z), highlighted with the signs Reference 201 and 202, respectively. As previously stated, cosine modulation for each channel results in a positive frequency filter and a negative frequency filter. In other words, the positive frequency filters 201 and 202 have corresponding negative frequency filters 203 and 204, respectively.

The p-modulation of the analysis filter Hp-i ( z), that is, Hp-i ( zWp) indicated by reference signs 211 and 213, is represented in Figure 2 (b) together with the synthesis filter Fp-i ( z), indicated by reference signs 201 and 203. In this Figure, reference sign 211 indicates the modulated version of the originally positive frequency filter Hpi ( z) and reference sign 213 indicates the modulated version of the originally negative frequency filter Hpi ( z). Due to p-order modulation, the negative frequency filter 213 moves to the positive frequency area and therefore overlaps with the positive synthesis filter 201. The shaded overlay 220 of the filters illustrates the energy of a term of main alias.

In Figure 2 (c) the p-modulation of Hp ( z), i.e. Hp ( zWp) indicated by reference signs 212 and 214, is shown together with the corresponding synthesis filter Fp ( z), signs reference 202 and 204. Again, the negative frequency filter 214 moves to the positive frequency area due to modulation of order p. The shaded area 221 again graphically shows the energy of a main alias term and, if not canceled, would typically result in significant overlap. To cancel the overlap, the term should be the reverse polarity copy of the overlap obtained from the intersection of the filters Hp-i ( zWp), 213, and Fp-i ( z), 201, of Figure 2 (b), that is, the reverse polarity copy of the shaded area 220. In a cosine modulated filter bank, where the gains are not changed, these main alias terms will usually cancel each other out entirely. However, in this example, the gain of the analysis (or synthesis) filter p is zero, so the overlap induced by the filters p - i will remain uncanceled on the output signal. An equally strong overlap residue will also arise in the negative frequency range.

When using complex exponential modulated filter banks, complex value modulation only results in positive frequency filters. Consequently, the main alias terms are gone, i.e. there is no significant overlap between the Hp ( zWp) modulated analysis filters and their corresponding Fp ( z) synthesis filters and the overlap can be significantly reduced when using such filter banks as equalizers. The resulting overlap depends solely on the degree of deletion of the remaining alias terms.

Therefore, even when using complex exponential modulated filter banks, it is essential to design a prototype filter for maximum deletion of alias profit terms, even though the main alias terms have been removed for such filter banks. Although the remaining alias terms are less significant than the main alias terms, they can still generate overlap that causes defects to the processed signal. Therefore, the design of such a prototype filter can preferably be achieved by minimizing a composite objective function. For this purpose, various optimization algorithms can be used. Some examples are linear programming methods, Downhill Simplex method or an unconstrained gradient based method, or other nonlinear optimization algorithms. In an exemplary embodiment, an initial solution is selected from the prototype filter. Using the composite objective function, one direction is determined to modify the prototype filter coefficients that provide the highest gradient of the composite objective function. The filter coefficients are then modified by using a given stage length, and the iterative procedure is repeated until a minimum of the composite objective function is obtained. For additional details on such optimization algorithms, reference is made to "Numerical Recipes in C, The Art of Scientific Computing, Second Edition" W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Cambridge University Press, NY, 1992.

For enhanced aliasing term minimization (IATM) of the prototype filter, a preferred objective function may be denoted

e, J a) ~ ae, + (i - «K, (30)

where the total error e ^tot ( a) is a weighted sum of the transfer function error e ^t and the overlap error ea. The first term on the right hand side (RHS) of Eq. (23) evaluated in the unit circle, i.e. for z = ei <ú, can be used to provide a measure of the error energy e ^t of the function transfer like

where P ( u>) is a symmetric real value function that defines the passband and nonpassband intervals, and D is the total delay of the system. In other words, P ( u>) describes the desired transfer function. In the most general case, said transfer function comprises a quantity that is a function of the frequency w. For a real value system Eq. (31) is simplified to

The objective function P ( w) and the objective delay D can be selected as an input parameter to the optimization procedure. The expression P ( w) e'JwD can be referred to as the objective transfer function.

A measure of the energy of total overlap ea can be calculated by evaluating the sum of the alias terms on the right hand side (RHS) of Eq. (23), i.e. the second term of Eq. (23), in the circle of unity like

For real value systems this translates into

In general, an optimization procedure to determine a prototype pa ( n) filter can be based on minimizing the error in Eq. (30). The parameter a can be used to distribute the emphasis between the transfer function and the overlap sensitivity of the prototype filter. While increasing the parameter a to 1 will place more emphasis on the transfer function error et, reducing the parameter a towards 0 will place more emphasis on the overlap error ea. The parameters P ( u>) and D can be used to establish an objective transfer function of the prototype filter p0 (n), that is, to define the behavior of the passband and non-passband and to define the overall delay of the system .

According to an example, a quantity of the filter bank channels k can be set to zero, e.g. For example, the top half of the filter bank channels are given zero gain. Consequently, the filter bank is encouraged to generate a large amount of overlap. This overlap will subsequently be minimized through the optimization process. In other words, by setting a certain number of filter bank channels to zero, the overlap will be induced, so as to generate an overlap error ea that can be minimized during the optimization procedure. Also, the complexity of optimization process calculations can be reduced by setting filter bank channels to zero.

According to an example, a prototype filter is optimized for a real value filter bank, that is, cosine modulated, which may be more appropriate than directly optimizing the complex value version. This is because actual value processing prioritizes distant overlap attenuation to a greater extent than complex value processing. However, when the overlap is driven as noted above, most of the induced overlap in this case will typically originate from terms that carry the main alias terms. Therefore, the optimization algorithm can spend resources on minimizing the main overlap that is not inherently present in the resulting complex exponential modulated system. In order to mitigate this, optimization can be done in a partially complex system; For alias terms that are free of major overlap, optimization can be accomplished through the use of actual value filter processing. On the other hand, the alias terms that the main alias terms would carry in a real value system would be modified for complex value filter processing. By means of such a partially complex optimization, the benefits of performing the processing can be obtained by using real-value processing, while the prototype filter is still optimized for use in a complex modulated filter bank system.

In an optimization example where exactly the top half of the filter bank channels are set to zero, the only alias term calculated from the complex value filters is the l = M / 2 term from Eq. (33). In this example, the function P ( u>) from Eq. (31), can be chosen as a unit magnitude constant that varies from -n / 2 + £ to n / 2- £, where £ is a fraction of n / 2, so as to cover the frequency interval that constitutes the passband. Outside the pass band the function P ( u>) can be defined to be zero or can be left undefined. In the latter case, the error energy of the transfer function Eq. (31) is only evaluated between -n / 2 + £ and n / 2- £. Alternatively and preferably, the passband error e ^t could be calculated on all channels k = 0, ..., M-1, from n through n with constant P ( u>) , even though the overlap is still calculated with multiple channels set to zero as described above.

Typically the optimization procedure is an iterative procedure, where given the prototype filter coefficients po ( n) ( n = 0, ..., N-1) at a given iteration stage, the target delay D, the number of channels M , the number of low band channels set to zero loCut, the number of high band channels set to zero hiCut and the weighting factor a, a value is calculated for the objective function for this iteration step. Through the use of semi-complex operations, this comprises the stages:

1. To obtain the passband error et, evaluate Eq. (32) in which P ( w) is a constant, by using

where H ^k ( eu) and F ^k ( j) are the DFT transforms of the analysis and synthesis filters h ^k ( n) and f ^k ( n) generated from the prototype filter coefficients in this stage of iteration of the Eq. (13) to (15), respectively.

2. To obtain the overlap error ea , for the overlap terms not subject to significant overlap, evaluate

where A ( eu) is calculated as

and H ^k ( el ^) and F ^k ( el ^) are the DFT transforms, that is, the z transforms evaluated in the unit circle, of the analysis and synthesis filters h ^k ( n) and fk (n) of Eq. (13) to (15).

3. For terms subject to significant overlap, evaluate

where Á ⁱ ( ew) is given by Eq. (24), with A ⁱ ( ew) as Eq. (37), where H ^k ( ew) and F ^k ( ew) are the DFT transforms of h ^k ( n) and f ^k ( n) of Eq. (19) and (20).

4. The error is later weighted with a as

ei „, (a) - ae, (1 - a ) {eaRí.al + e aCplx). (39)

By using any of the nonlinear optimization algorithms referred to above, this total error is reduced by modifying the prototype filter coefficients, until an optimal set of coefficients is obtained. As an example, the direction of the largest gradient of the error function e ^tot is determined for the prototype filter coefficients at a given iteration stage. By using a certain stage size the prototype filter coefficients are modified in the direction of the largest gradient. The modified prototype filter coefficients are used as a starting point for the subsequent iteration stage. This procedure is repeated until the optimization procedure has converged to a minimum value of the error function e ^tot .

An example optimization procedure is illustrated in Figure 3 as a flowchart 300. In a parameter determination step 301 the parameters of the optimization procedure are defined, ie in particular the target transfer function comprising the delay target D , the number of bank channels M of target filters, the number N of coefficients of the prototype filter, the weighting parameter a of the objective error function, as well as the parameters for the generation of overlap, that is, loCut and / or hiCut. In an initialization step 302, a first set of prototype filter coefficients is selected.

In the passband error determining unit 303, the passband error term e ^{t is determined} by using the given set of coefficients of the prototype filter. This can be done by using Eq. (32) in combination with Eqs. (35) and (13) through (15). In the actual value overlap error determining unit 304, a first part e ^aReai of the overlap error term e ^a can be determined by using Eqs. (36) and (37) in combination with Eqs. ( 13) to (15). Also, the determination unit aliasing error complex value 305 can be determined a second part and ^aCpix of the error term overlap and ^to using Eq. (38) in combination with Eq. (19) and (20). As a consequence, the objective function e ^tot can be determined from the results of units 303, 304, and 305 by using Eq. (39). Nonlinear optimization unit 306 uses optimization methods, such as linear programming, so as to reduce the value of the objective function. By way of example, this can be done by determining a possibly maximum gradient of the objective function with respect to modifications of the prototype filter coefficients. In other words, modifications of the prototype filter coefficients that result in a possible maximum reduction in objective function can be determined.

If the gradient determined in unit 306 remains within the predetermined limits, decision unit 307 decides that a minimum of the objective function has been reached and ends the optimization procedure in step 308. If on the other hand the gradient exceeds the default value, then the prototype filter coefficients are updated in the update unit 309. The update of the coefficients can be done by modifying the coefficients with a predetermined step in the direction given by the gradient. Finally, the updated prototype filter coefficients are reinserted as an input to the step band error determination unit 303 for another iteration of the optimization procedure.

In general, it can be stated that by using the above error function and an appropriate optimization algorithm, prototype filters can be determined which are optimized with respect to their degree of perfect reconstruction, i.e. with respect to low overlap in combination with low phase and / or amplitude distortion, its resilience to overlap due to subband modifications, its system delay and / or its transfer function. The design method provides parameters, in particular a weighting parameter a, a target delay D, a target transfer function P ( w), a filter length N, a number of filter bank channels M, as well as parameters that They drive overlapping hiCut, loCut, which can be selected to obtain an optimal combination of the filter properties mentioned above. Also, zeroing a certain number of subband channels, as well as partial complex processing, can be used to reduce the overall complexity of the optimization procedure. As a result, asymmetric prototype filters with near-perfect reconstruction property, low overlap sensitivity, and low system delay can be determined for use in a complex exponential modulated filter bank. It should be noted that the previous determination scheme of a prototype filter has been indicated in the context of a filter bank modulated by complex exponential. If other filter bank design methods are used, e.g. ex. cosine or sine modulated filter bank design methods, then the optimization procedure can be adapted by generating the analysis and synthesis filters h ^k ( n) and f ^k ( n) by using design method design equations of respective filter bank. By way of example, Eqs. (13) to (15) can be used in the context of a cosine modulated filter bank.

The following is a detailed example of a 64 channel low delay filter bank. By using the proposed optimization method mentioned above, a detailed example of a 64-channel, low delay, aliased gain term filter bank (M = 64) will be pointed out. In this example the partially complex optimization method has been used and the upper 40 channels have been set to zero during the prototype filter optimization, that is, hiCut = 40, while the loCut parameter remained unused. Therefore, all the alias profit terms, except A ⁱ , where l = 24, 40, are calculated using real value filters. The total system delay is chosen as D = 319, and the prototype filter length is N = 640. A time domain graph of the resulting prototype filter is given in Figure 4 (a), and the frequency response of the prototype filter It is represented in Figure 4 (b). The filter bank offers a passband reconstruction error (amplitude and phase) of -72 dB. The phase deviation from a linear phase is less than ± 0.02 °, and the overlap suppression is 76 dB when no modifications are made to the subband samples. The actual filter coefficients are tabulated in Table 1. It should be noted that the coefficients are scaled by a factor M = 64 with respect to other equations in this document that depend on an absolute scaling of the prototype filter.

Although the above description of the filter bank design is based on a standard filter bank notation, an example to operate the designed filter bank can operate on other descriptions or notations of bank filters, e.g. eg, filter bank implementations that allow for more efficient operation in a digital signal processor.

In one example, the steps for filtering a time domain signal using an optimized prototype filter can be described as follows:

In order to operate the filter bank efficiently, the prototype filter, i.e., po ( n) from Table 1, is first arranged in the polyphase representation, where all other polyphase filter coefficients are negated and all the coefficients change over time as

/> Ó (639-128 »! - n) - (- l) mpo (128m n), 0 < n <128.0 < m <5 (40)

The analysis stage begins with the polyphasic representation of the filter that is being applied to the time domain signal x ( n) to produce a vector xi ( n) of length 128 as

xP7, {k) = t, A ,, (128m /) x (128ffl / 64 ??), 0 </ <128, n = 0.1, ... (41)

nor -0

xi ( n) is subsequently modified with a modulation matrix like

127

0 < k < 64, (42) vk ( n ) = £

0 < k < 64, (42)

where v ^k ( n), k = 0 ... 63, constitute the subband signals. The time index n is given accordingly in subband samples.

Complex value subband signals can then be modified, eg. For example, according to some desired equalization curve gk (n), possibly variable in time and of complex value, such as

The synthesis stage begins with a demodulation stage of the modified subband signals as

/ - (A - + - X2 / -255) 0 </ <128. (44)

128 2

128 2

It should be noted that the modulation stages of Eqs. (42) and (44) can be achieved in a very efficient computational way with fast algorithms that use fast Fourier transform (FFT) kernels.

The demodulated samples are filtered with the polyphasic representation of the prototype filter and accumulated to the output time domain signal x (n) according to

j (128m / 64 «) - í (128 /? ¡/ 64 n) + /? '(639- 128 ^íh - I) ui (/),

⁽ Four. Five ⁾

0 </ <128, 0 <? H <5, «= 0.1, ...

where x ( n) is set to 0 for all n at start time.

It should be noted that both floating point and fixed point implementations can change the numerical precision of the coefficients given in Table 1 to something more suitable for processing. Without limiting the scope, values can be quantified to a lower numerical precision by rounding, truncation, and / or scaling the coefficients to integers or other representations, in particular representations that fit the available resources of a hardware platform and / or or software in which the filter bank must operate.

Likewise, the previous example indicates the operation in which the time domain output signal is of the same sampling frequency as the input signal. Other implementations can resample the time domain signal by using different sizes, ie different channel count, from the analysis and synthesis filter banks, respectively. However, filter banks should be based on the same prototype filter and are obtained by resampling the original prototype filter through decimation or interpolation. As an example, a prototype filter for a 32-channel filter bank is accomplished by resampling the coefficients po ( n) as

1

^ / 2, (0 = -b or (2 / T Í) A, (26]. 0 </ <320.

The length of the new prototype filter is therefore 320 and the delay is

^{D = | _319 / 2 J = 159} _{where the operator} L-J _{returns the integer part of its argument.}

Table 1 Coefficients of a 64-channel low-delay prototype filter

Different aspects of practical implementations are outlined below. Using standard PC or DSP, real-time operation of a low-delay complex exponential modulated filter bank is possible. The filter bank may also be encoded on a custom chip. Figure 5 (a) shows the structure for an effective implementation of the analysis part of a complex exponential modulated filter bank system. The analog input signal is first fed to an A / D converter 501. The digital time domain signal is fed to a shift register containing 2M samples that shift M samples at a time 502. Then the shift register signals are they filter through the polyphase coefficients of the prototype filter 503. The filtered signals are subsequently combined 504 and in parallel transformed with a DCT-IV 505 and DST-IV 506 transform. The outputs of the cosine and sine transforms constitute the real parts and imaginary of the subband samples respectively. The gains of the subband samples are modified according to the current setting of the 507 Spectral Envelope Adjuster.

An efficient implementation of the synthesis part of a low delay complex exponential modulated system is shown in Figure 5 (b). The subband samples are first multiplied with complex value spin factors, i.e. constants dependent on the complex value channel, 511, and the real part is modulated with a DCT-IV transform 512 and the imaginary part with a DST-transform. IV 513. The outputs of the transforms are combined 514 and fed through the multiphase components of the prototype filter 515. The time domain output signal is obtained from the shift register 516. Finally, the digital output signal it is converted back to a 517 analog waveform.

While the implementations noted above use DCT and DST type IV transforms, implementations using DCT type II and III kernels are equally possible (and also DST type II and III based implementations). However, the most computationally efficient implementations for complex exponential modulated banks use pure FFT kernels. Implementations using direct vector matrix multiplication are also possible but are less efficient.

In summary, this document describes a design method for prototype filters used in analysis / synthesis filter banks. The desired properties of the prototype filters and the resulting analysis / synthesis filter banks have near perfect reconstruction, low delay, low sensitivity to overlap, and minimal amplitude / phase distortion. An error function is proposed that can be used in an optimization algorithm to determine appropriate coefficients of the prototype filters. The error function comprises a set of parameters that can be adjusted to change the emphasis between the desired filter properties. Asymmetric prototype filters are preferably used. Also, a prototype filter is described that provides a good reconciliation of desired filter properties, ie near perfect reconstruction, low delay, high overlap resilience and minimal phase / amplitude distortion.

Although specific applications and embodiments have been described herein, it will be apparent to those skilled in the art that various variations of the applications and embodiments described herein are possible without departing from the scope of the invention described and claimed herein. . It should be understood that although certain forms of the invention have been shown and described, it should not be limited to the specific embodiments described and shown or the specific methods described.

The filter design method and system as well as the filter bank described in this document can be implemented as software, firmware and / or hardware. Certain components can be implemented, eg. eg, as software running on a digital signal processor or microprocessor. Other components can be implemented, eg. eg as hardware or application specific integrated circuits. The signals found in the described methods and systems can be stored in media such as random access memory or optical storage media. They can be transferred via networks, such as radio networks, satellite networks, wireless networks or wired networks, eg. eg the Internet. Typical devices that make use of the filter banks described in this document are decoders or other equipment of customer facilities that decode audio signals. On the coding side, filter banks can be used in broadcasters, eg. eg, bedside video systems.

Claims (7)

1. A signal processing device for filtering and performing high frequency reconstruction of an audio signal, wherein the signal processing device comprises: an analysis filter bank that receives true value time domain input audio samples and generates complex value subband samples; a unit that generates modified complex value subband samples by modifying gains of complex value subband samples according to the current setting of the spectral envelope adjuster; Y a synthesis filter bank that receives the modified complex value subband samples and generates time domain output audio samples, where the synthesis filter bank comprises M synthesis filters fk (n) that are complex exponential modulated versions of a prototype filter p0 (n) according to:

where the analysis filter bank comprises K analysis filters, with K different from M, which are complex exponential modulated versions of a prototype filter obtained from the prototype filter p0 (n) by resampling the prototype filter p0 (n) through decimation or interpolation, where the prototype filter p0 (n) has a length N, and where the analysis filter bank and the synthesis filter bank have a system delay of D samples. 2. The signal processing device of claim 1, wherein the prototype filter p0 (n) is a prototype symmetric low-pass filter or a prototype asymmetric low-pass filter. 3. The signal processing device of claim 1, wherein the analysis filter bank is a pseudo QMF bank. 4. The signal processing device of claim 1, wherein an order of the prototype filter p0 (n) equals the delay of system D. 5. The signal processing device of claim 1, wherein the number of channels in the analysis filter bank is 32 and the number of channels in the synthesis filter bank is 64. 6. A method performed by a signal processing device for filtering and performing high frequency reconstruction of an audio signal, wherein the method comprises: receive real-time time domain input audio samples; filter the actual value time domain input audio samples with an analysis filter bank to generate complex value subband samples; generating modified complex value subband samples through a high frequency reconstruction process by modifying gains of complex value subband samples according to the current configuration of the spectral envelope adjuster; filter the modified complex value subband samples with a synthesis filter bank to generate time domain output audio samples, where the synthesis filter bank comprises M synthesis filters fk (n) that are complex exponential modulated versions of a prototype filter p0 (n) according to:

where the analysis filter bank comprises K analysis filters, with K different from M, which are complex exponential modulated versions of a prototype filter obtained from the prototype filter p0 (n) by resampling the prototype filter p0 (n) through decimation or interpolation, where the prototype filter p0 (n) has a length N, and where the analysis filter bank and the synthesis filter bank have a system delay of D samples. 7. A non-transient computer-readable medium containing instructions that when executed by a processor perform the method of claim 6.