KR20190099094A - Complex exponential modulated filter bank for high frequency reconstruction or parametric stereo - Google Patents

Abstract

This document relates to modulated and sub-sampled digital filter banks, as well as methods and systems for the design of such filter banks. In particular, this document proposes a method and apparatus for the improvement of low delay modulated digital filter banks. The method utilizes the modulation of the asymmetric lowpass prototype filter and a new method for optimizing the coefficients of the filter. Moreover, a specific design is provided for channel filter bank 64 using the prototype filter length of coefficients 640 and the system delay of samples 319. The method substantially reduces artifacts due to aliasing resulting from independent changes in subband signals, for example when using a filter bank as a spectral equalizer. The method is preferably implemented in software running on a standard PC or digital signal processor (DSP), but can also be hardcoded on a custom chip. The method provides improvements to spectral envelopes that adjust filter banks used in various types of digital equalizers, adaptive filters, multiband comparators and high frequency reconstruction (HFR) or parametric stereo systems.

Description

COMPLEX EXPONENTIAL MODULATED FILTER BANK FOR HIGH FREQUENCY RECONSTRUCTION OR PARAMETRIC STEREO}

The present invention relates to digital filter banks that are modulated and sub-sampled, as well as methods and systems for the design of such filter banks. In particular, the present invention is a novel design method and apparatus for an almost complete recovery low delay cosine or complex exponential modulated filter bank that is optimized for suppression of aliasing resulting from changes in subband signals or spatial coefficients. To provide. Moreover, a specific design for a 64 channel filter bank is provided using a prototype filter length of 640 coefficients and a system delay of 319 samples.

The contents of this document are described, for example, in US N.Y. Digital equalizers as outlined in A.J.S.Ferreira, J.M.N.Viera's "An Efficient 20 Band Digital Audio Equalizer" at the AES preprint 98th Convention, February 25-28, 1995; See, for example, A.Gilloire, M. Vetterli's Adaptive Filtering in Subbands with Critical Sampling: Analysis, Experiments, and Application to Acoustic Echo Cancellation in August 1992, IEEE Transactions on Signal Processing, vol. 40, no. Adaptive filters as outlined, multiband comparators, and audio coding systems using high frequency reconstruction (HFR) methods; or audio coding systems using so-called parametric stereo techniques. In the latter two examples, the digital filter bank is used for adaptive adjustment of the spectral envelope of an audio signal The exemplary HFR system is for example the Spectral Band Replication (SBR) system outlined in WO98 / 57436. Parametric stereo system is described, for example, in EP1410687.

Within the specification, including the claims, the expressions "subband signals" or "subband samples" refer to an output signal or output signals, or an output sample or output samples or transform based from an analysis portion of the digital filter bank. Represents the system's forward transform, that is, the output from a transform computed on time domain data. Examples of the output of such forward transforms include the analysis of frequency domain coefficients from a windowed digital Fourier transform (DFT) or a modified discrete cosine transform (MDCT). Output samples from

Within the present specification, including the claims, the expression “aliasing” is a reduction, possibly combined with a change (eg, attenuation or quantization) of subband samples in a sub-sampled digital filter bank. And nonlinear distortion resulting from interpolation.

The digital filter bank is a collection of two or more parallel digital filters. The analysis filter bank separates the incoming signal into a number of distinct signals or spectral coefficients called subband signals. The filter bank is critically sampled or maximized when the total number of subband samples per unit time is equal to the total number for the input signal. A so-called synthesis filter bank combines the subband signals into the output signal. Popular types of critically sampled filter banks are cosine modulated filter banks, where the filters are obtained by cosine modulation of a low pass filter, the so-called prototype filter. Cosine modulated filter banks provide efficient implementations and are commonly used in natural audio coding systems. For more details, see "Introduction to Perceptual Coding" by K. Brandenburg in 1996 AES, Collected Papers on Digital Audio Bitrate Reduction.

A common problem in filter bank design is that any attempt to change subband samples or spectral coefficients, for example by applying an equalizing gain curve or by quantizing subband samples, typically results in aliasing artifacts to the output signals. To render them. Therefore, filter bank designs that reduce such artifacts, even when the subband samples undergo severe changes, are desirable.

A possible way is to use oversampled, ie critically unsampled filter banks. An example of an oversampled filter bank is a class of filter banks that are modulated with a complex exponent, where the imaginary sine modulation portion is added to the real part of the cosine modulated filter bank. Such complex exponential modulated filter banks are described in EP1374399, which is incorporated herein by reference.

One of the properties of complex exponential modulated filter banks is that they are free from the main aliasing terms present in the cosine modulated filter banks. As a result, such filter banks are typically less prone to artifacts induced by changes to subband samples. Nevertheless, complex design techniques must be applied to the prototype filter of such complex exponentially modulated filter banks in order to minimize other aliasing terms and to minimize obstacles such as aliasing resulting from changes in subband signals.

An additional property of filter banks is the amount of delay that occurs when a signal passes through such filter banks. Especially for real-time applications, such as audio and video streams, the filter or system delay should be low. A possible way to obtain a filter bank with a low total system delay, i.e. a low delay or latency of signals passing through the analysis filter bank before the synthesis filter bank, is to use short symmetric prototype filters. Typically, using short prototype filters results in relatively poor frequency band separation characteristics resulting in wide frequency overlap regions between adjacent subbands. As a result, short prototype filters typically do not allow filter bank design to adequately suppress aliasing when modifying subband samples and other methods for the design of low delay filter banks are required.

It would therefore be desirable to provide a design method for filter banks that combines a certain number of desirable attributes. Such attributes may include high levels of insensceptibility to signal impairments such as aliasing that have undergone changes in subband signals; Low delay or latency of signals passing through the analysis and synthesis filter banks; And good approximation for complete recovery attributes. In other words, it is desirable to provide a design method for filter banks that generate low levels of errors. Subsampled filter banks typically produce linear distortion from a passband term that can be further divided into two types of errors, amplitude and phase errors, and non-linear distortion resulting from aliasing terms. Although the "good approximation" of the PR (perfect reconstruction) attribute keeps all of these errors at a low level, it may be advantageous to emphasize more the reduction of distortions caused by aliasing in terms of recognition.

Furthermore, 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. It is also desirable for the property of the filter bank to exhibit a nearly constant group delay to minimize artifacts due to phase dispersion of the output signal.

This document considers markedly by using a filter bank design method in which damages resulting from changes in subband signals are called an improved alias term minimization (IATM) method for the optimization of symmetric or asymmetric prototype filters. It can be reduced.

The present invention teaches that the concepts of pseudo Quadrature Mirror Filter (QMF) designs, ie, nearly complete recovery filter bank designs, can be extended to cover a low delay filter bank system using asymmetric prototype filters. As a result, nearly complete recovery filter banks can be designed with low levels of passband errors including low system delay, low sensitivity to aliasing, and / or phase dispersion. Depending on the particular needs, the emphasis placed on either of the filter bank attributes can be changed. Therefore, the filter bank design method according to the present invention alleviates the current limitations of the PR filter banks used in an equalization system or another system that changes the spectral coefficients.

The design of the low delay complex exponential modulation filter bank according to this document consists of the following steps:

Design of an asymmetric lowpass prototype filter with a cutoff frequency of π / 2M, optimized for desired aliasing and passband error rejections, and further optimized for system delay D; M is the number of channels in the filter bank; And

May comprise the construction of an M-channel filter bank by complex exponential modulation of the optimized prototype filter.

Moreover, the operation of such a low delay complex exponential modulated filter bank in accordance with this document comprises the following steps:

Filtering of the real-time time domain signal of the real value through an analysis of the filter bank;

Changing, for example, the complex valued subband signals according to the desired, possibly time varying, equalizer setting;

Filtering of the changed complex valued subband samples through the synthesis section of the filter bank; And

May include calculation of the real part of the complex valued time domain output signal obtained from the synthesis part of the filter bank.

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

The contents of the present invention, in particular the filter banks designed according to the proposed filter bank and the proposed design method, can be used in various applications. Such applications are an improvement over the adaptive envelope that adjusts filter banks used in various types of digital equalizers, adaptive filters, multiband comparators and HFR or parametric stereo systems.

According to a first aspect, a method for determining N coefficients of an asymmetric prototype filter p ₀ used to construct an M-channel, low delay, subsampled analysis / synthesis filter bank is described. The analysis / synthesis filter bank may include M analysis filters h _k and M synthesis filters f _k , where k takes values from 0 to M-1 and M is typically greater than one. The analysis / synthesis filter bank typically has an overall transfer function associated with the reduction and interpolation operations as well as the coefficients of the analysis and synthesis filters.

The method includes selecting a target transfer function of a filter bank comprising a target delay (D). Typically a target delay D less than or equal to N is selected. The method further includes determining a composite objective function e _tot comprising a pass band error term e _t and an aliasing error term e _a . The passband error term is associated with the deviation between the transfer function and the target transfer function of the filter bank and the aliasing error term e _a is associated with the errors caused by subsampling, i.e., the reduction and / or interpolation of the filter bank. In a further method step, N coefficients of the asymmetric prototype filter p ₀ that reduce the synthesis objective function e _tot are determined.

Typically, determining the objective error function e _tot and determining the N coefficients of the asymmetric prototype filter p ₀ are repeated repeatedly until the minimum value of the objective error function e _tot is reached. do. That is, the objective function e _tot is determined based on the given set of coefficients of the prototype filter, and the updated set of coefficients of the prototype filter is generated by reducing the objective error function. This process is repeated until further reduction of the objective function cannot be achieved by changing the prototype filter coefficients. This may include determining the objective error function e _tot and determining the value for the synthesis objective function e _tot for the given coefficients of the prototype filter p ₀ and using the asymmetric prototype filter ( determining an updated coefficient of the step of determining the N coefficients of p ₀₎ prototype filter (the prototype filter (p ₀₎ based on the slope of the composite objective function (e _tot) which is associated with a coefficient p ₀₎ It may include the step.

According to a further aspect, the synthesis objective error function e _tot is:

e _tot (α) = αe _t + (1-α) e _a

Provided by

Where e _t is the passband error term, e _a is the aliasing error term, and α is a weighting constant that takes values between 0 and 1. The passband error term e _t can be determined by accumulating the squared deviation between the target transfer function and the transfer function of the filter bank for the plurality of frequencies. In particular, the passband error term e _t is

Can be calculated as

Where P (ω) e ^-jwD is the target transfer function,

Where H _k (z) and F _k (z) are the z-transformations of the analytical and synthesis filters h _k (n) and f _k (n), respectively.

The aliasing error term e _a is determined by accumulating the squared magnitude of the alias gain terms for the plurality of frequencies. In particular, the aliasing error term e _a

Calculated as

, l = 1 ... M-1이고,Where z = e ^jω ,

, l = 1 ... M-1,

Is the l th alias gain term obtained from the unit circle with W = e ^{-i2π / M} , where H _k (z) and F _k (z) are the analysis and synthesis filters h _k (n) and f _k ( n) each of the z-transformations. The notation A _l * (z) is the z-transformation of the complex conjugate sequence a _l (n).

According to a further aspect, the step of determining a value for the synthesis objective function e _tot is an analysis / synthesis based on the prototype filter p ₀ (n) using cosine modulation, sine modulation and / or complex exponential modulation. Generating analysis filters h _k (n) and synthesis filters f _k (n) of the filter bank. In particular, analysis and synthesis filters utilize cosine modulation.

Can be determined as

Where n = 0 ... N-1 for the M analytic filters of the analytic filter bank;

And wherein for M synthesis filters in the synthesis filter bank, n = 0 ... N-1.

Analysis and synthesis filters also provide complex exponential modulation

Can be determined using

Where n = 0 ... N-1 and A is any constant for the M analysis filters of the analysis filter bank;

Where n = 0 ... N-1 for the M synthesis filters in the synthesis filter bank.

According to another aspect, determining the values for the synthesis 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, ie filter coefficients h _k and / or f _k can be set to zero for at least one channel k. have. In an example the predetermined number of low frequency channels and / or the predetermined number of high frequency channels may be set to zero. That is, at low frequency filter bank channels k = 0, the maximum C _low (where C _low is greater than zero) may be set to zero. Alternatively or additionally, at high frequency filter bank channels k = C _high , the maximum M-1, where C _high is less than M-1, can be set to zero.

In such a case, determining the value for the synthesis objective function e _tot comprises analyzing and synthesis filters on the aliasing terms C _low and MC _low and / or C _high and MC _high using complex exponential modulation. And generating them. This may further include analysis and synthesis filters for the remaining aliasing terms using cosine modulation. That is, the optimization procedure can be done in a partially complex valued manner, where an aliasing error term free from main aliasing is calculated using real valued filters, for example filters generated using cosine modulation, and real valued. The aliasing error terms with primary aliasing in the system of are changed for processing of complex values using, for example, complex exponential modulation filters.

According to a further aspect, the analysis filter may generate M subband signals from the input signal using M analysis filters h _k . These M subband signals may be abbreviated by factor M to yield abbreviated subband signals. Typically, the abbreviated subband signals are altered, for example, for equalization purposes or compression purposes. Possible alternating shortened subband signals may be upsampled by factor M and the synthesis filter bank may generate an output signal from the upsampled shortened subband signals using M synthesis filters f _k .

According to another aspect, an asymmetric prototype filter comprising coefficients derivable from the coefficients of Table 1 by any one of rounding, truncating, scaling, subsampling or oversampling ( p ₀ (n)) is described. Any combination of rounding, truncating, scaling, subsampling or oversampling is possible.

The rounding operation of the filter coefficients may include one of the following: more than 20 significant digits; More than 19 significant digits; More than 18 significant digits; More than 17 significant digits; More than 16 significant digits; More than 15 significant digits; More than 14 significant digits; More than 13 significant digits; More than 12 significant digits; More than 11 significant digits; More than 10 significant digits; More than 9 significant digits; More than 8 significant digits; More than 7 significant digits; More than 6 significant digits; More than 5 significant digits; More than 4 significant digits; More than 3 significant digits; More than 2 significant digits; More than 1 significant digits; Rounding to 1 significant digit.

The truncating operation of the filter coefficients may include one of the following: more than 20 valid digits; More than 19 significant digits; More than 18 significant digits; More than 17 significant digits; More than 16 significant digits; More than 15 significant digits; More than 14 significant digits; More than 13 significant digits; More than 12 significant digits; More than 11 significant digits; More than 10 significant digits; More than 9 significant digits; More than 8 significant digits; More than 7 significant digits; More than 6 significant digits; More than 5 significant digits; More than 4 significant digits; More than 3 significant digits; More than 2 significant digits; More than 1 significant digits; 1 Truncating to valid digits.

The scaling operation of the filter coefficients may include up-scaling and down-scaling of the filter coefficients. In particular, this may include up and / or down-scaling by the number M of filter bank channels. Such up- and / or down-scaling can be used to maintain the input energy of the input signal in the filter bank at the output of the filter bank.

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

The oversampling operation is a factor less than or equal to 2, a factor less than or equal to 3, a factor less than or equal to 4, a factor less than or equal to 5, a factor less than or equal to 6, a factor less than or equal to 7, a factor less than or equal to 8 It may include oversampling by the same factor, a factor less than or equal to 9, and a factor less than or equal to 10. The oversampling operation may further include the determination of the oversampled filter coefficients by interpolation between two adjacent filter coefficients.

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

According to another aspect, a method for generating abbreviated subband signals with low sensitivity to aliasing resulting from changes in subband signals is described. The method includes determining analysis filters of an analysis / synthesis filter bank according to the methods outlined herein; Filtering a real valued time domain signal through the analysis filters to obtain complex valued subband signals; And shortening the subband signals. Moreover, a method for generating a real valued output signal from a plurality of complex valued subband signals having low sensitivity to aliasing resulting from changes in subband signals is described. The method includes determining synthesis filters of an analysis / synthesis filter bank that are different from the methods outlined herein; Interpolating the plurality of complex valued subband signals; Filtering the plurality of interpolated subband signals through the synthesis filters; Generating a complex valued time domain output signal as the sum of the signals obtained from said filtering; And taking the real part of the complex valued time domain output signal as the real valued output signal.

In another aspect, a system is described that operates to generate subband signals from a time domain input signal, wherein the system is generated in accordance with the methods outlined herein and / or based on prototype filters outlined herein. Include an analysis filter bank.

It should be noted that aspects of methods and systems including their own preferred embodiments as outlined in this patent application may be used alone or in combination with other aspects of the methods and systems disclosed herein. . Moreover, all aspects of the methods and systems outlined in this patent application may be arbitrarily combined. In particular, the features of the claims may be combined with one another in any way.

1 shows the analysis and synthesis sections of a digital filter bank.
FIG. 2 shows normalized frequency responses for a set of filters to illustrate the adverse effects of changing subband samples in a cosine modulated, ie, real valued filter bank.
3 shows a flowchart of an example of an optimization procedure.
4 shows a time domain plot and frequency response of an optimized prototype filter for a low delay modulation filter bank with 64 channels and a system delay of 319 samples in total.
5 shows an example of analysis and synthesis sections of a low delay complex exponential modulated filter bank system.

The invention will now be described by means of illustrative examples which do not limit the scope with reference to the accompanying drawings.

It is to be understood that the subject matter is applicable to the scope of implementations incorporating other digital banks than those expressly mentioned in this patent. In particular, the contents may be applicable to other methods for designing a filter bank based on a prototype filter.

Next, the overall transfer function of the analysis / synthesis filter bank is determined. That is, a mathematical representation of the signal passing through such a filter bank system is described. A digital filter bank is a collection of Ms, where M are two or more parallel digital filters that share a common input or common output. For details on such filter banks, reference is made to "Multirate Systems and Filter Banks" by PP Vaidyanathan Prentice Hall: Englewood Cliffs, NJ, 1993. When sharing a common input, a filter bank can be called an analysis bank. The analysis bank separates the incoming signal into M separate signals called subband signals. Analytical filters are _denoted by H _k (z), where k = 0, .., M-1. The filter bank is truncated to the maximum when it is critically sampled or when the subband signals are abbreviated by factor M. Therefore, the total number of subband samples per time unit over all subbands is equal to the number of samples per time unit for the input signal. The synthesis bank combines these subband signals with common output signals. The synthesis filters are denoted F _k (z), for k = 0, ..., M-1.

)로 재합성한다.A maximally abbreviated filter bank with M channels is shown in FIG. 1. The analyzer 101 calculates, from the input signal X (z), subband signals V _k (z) constituting signals to be transmitted, stored or changed. The synthesis unit 102 outputs a signal V _k (z) to an output signal (

Resynthesize with).

)를 획득하기 위한 V_k(z)의 재합성은 여러 잠재적인 에러들을 겪는다. 에러들은 완전한 복구 속성의 근사로 인한 것일 수 있고 서브대역들의 축약 및 보간에 의해 발생될 수 있는 에일리어싱으로 인한 비-선형 손상들을 포함한다. 완전 복구 속성의 근사들로 인한 다른 에러들은 위상 및 진폭 왜곡과 같은 선형 손상들로 인한 것일 수 있다.Approximation of the original signal (X (z))

_Resynthesis of V _k (z) to obtain) suffers from several potential errors. Errors can be due to an approximation of the complete recovery attribute and include non-linear damages due to aliasing that can be caused by shortening and interpolation of subbands. Other errors due to approximations of the full recovery attribute may be due to linear impairments such as phase and amplitude distortion.

According to the notation of FIG. 1, the output of the analysis filters H _k (z) 103 is

Where k = 0, ..., M-1. Decimators 104, also referred to as down-sampling unit, are outputs.

, Where W = e ^{-i2π / M.} The output of interpolators 105, also called up-sampling units,

Provided by

The sum of the signals obtained from the synthesis filters 106 is

Can be written as

가 변조된 입력 신호(X(zW^l)) 및 대응하는 에일리어스 이득 항(A_l(z))의 적(product)으로 구성되는 M개의 성분들의 합임을 나타낸다. 식 (4)는Is the gain for the l-th aliasing term X (zW ^l ). Equation (4) is

Denotes the sum of M components consisting of the product of the modulated input signal X (zW ¹ ) and the corresponding alias gain term A ₁ (z). Equation (4) is

Can be rewritten.

The last sum of the right hand side (RHS) constitutes the sum of all unwanted alias terms. Elimination of all aliases to make this sum to zero through the appropriate choices of H _k (z) and F _k (z)

Providing

here

Is the entire transfer function or the distortion function. Equation (8) shows that, according to H _k (z) and F _k (z), T (z) is free from both phase distortion and amplitude distortion. The overall transfer function is in this case simply the delay of the D samples with a constant scale factor c, i.e.

Will be replaced by equation (7),

To provide.

The types of filters that satisfy Eq. (10) are said to have perfect reconstruction (PR) properties. If equation (10) is approximately satisfied but not completely satisfied, the filters belong to the class of approximate fully reconstructed filters.

Next, a method for designing analysis and synthesis filter banks from a prototype filter is described. The resulting filter banks are called cosine modulated filter banks. In the conventional theory of cosine modulated filter banks, the analysis filters h _k (n) and the synthesis filters f _k (n) are cosine modulated versions of the symmetric low pass prototype filter p ₀ (n), ie respectively.

Where M is the number of channels in the filter bank and N is the prototype filter order.

The cosine modulation analysis filter bank produces real valued subband samples for real valued input signals. Subband samples are down sampled by factor M, allowing the system to be sampled critically. Depending on the choice of the prototype filter, the filter bank constitutes an approximate complete reconstruction system, ie a so-called pseudo QMF bank or a complete reconstruction (PR) system, for example described in US5436940. An example of a PR system is a modulated lapped transform (MLT) described in more detail in HSMalvar's "Lapped Transforms for Efficient Transform / Subband Coding" in IEEE Trans ASSP, vol. 38, no. 6, 1990. . The total delay, or system delay, for a conventional cosine modulated filter bank is N.

In order to obtain filter bank systems with lower system delays, this document teaches to replace symmetric prototype filters used in conventional filter banks with asymmetric prototype filters. In the prior art, the design of asymmetric prototype filters has been limited to systems with perfect reconstruction (PR) properties. A full reconstruction system using such asymmetric prototype filters is described in EP0874458. However, the full reconstruction limit imposes limits on the filter banks used in the equalization system, for example, due to the limited degree of freedom in designing the prototype filter. It should be noted that symmetric prototype filters have a linear phase, that is, they have a constant group delay over all frequencies. On the other hand, asymmetric filters typically have a nonlinear phase, i.e. they have a group delay that can vary with frequency.

In filter bank systems using asymmetric prototype filters, the analysis and synthesis filters are respectively

및

는 각각 길이들(N_h 및 N_f)의 분석 및 합성 프로토타입 필터들이고, D는 필터 뱅크 시스템의 총 지연이다. 범위를 제한하지 않고, 다음에서 연구되는 변조 필터 뱅크들은 분석 및 합성 프로토타입들이 동일한 시스템들, 즉Can be written as

And

Are the analysis and synthesis prototype filters of lengths N _h and N _f , respectively, and D is the total delay of the filter bank system. Without limiting the range, the modulation filter banks studied in the following are systems that have the same analysis and synthesis prototypes,

Where N is the length of the prototype filter p ₀ (n).

However, it should be noted that when using the filter design approaches outlined in this document, filter banks using different analytical and synthetic prototype filters can be determined.

은 코사인 변조 필터 뱅크들에서의 주 에일리어싱 항들의 소거를 제공하도록 선택된다. 그럼에도 불구하고, 서브대역 샘플들을 변경하면, 주 에일리어스 항들의 소거가 되지 않음으로써, 주 에일리어스 항들로부터 에일리어싱의 강한 영향력이 발생하게 된다. 그러므로 서브대역 샘플들로부터의 이 주 에일리어스 항들을 완전하게 제거하는 것이 바람직하다.An inherent property of cosine modulation is that every filter has two passbands; One pass band in the positive frequency range and the corresponding pass band in the negative frequency range. The so-called major, or effective, alias terms are between the negative pass bands of the filter with frequency modulated versions of the positive pass bands, or vice versa, the positive pass band of the filter with frequency modulated versions of the negative pass bands. What happens as the frequency overlaps between them can be verified. Last term in equations (13) and (14), i.e. terms

Is selected to provide cancellation of main aliasing terms in cosine modulated filter banks. Nevertheless, changing the subband samples does not cancel the primary alias terms, resulting in a strong influence of aliasing from the primary alias terms. Therefore, it is desirable to completely remove this main alias term from the subband samples.

Elimination of the main aliasing terms can be achieved by the use of so-called complex exponential modulation filter banks based on the extension of cosine modulation to complex exponential modulation. Such extension uses the same notation as before to analyze the analysis filters h _k (n).

Calculate This may be considered to add an imaginary part to the real valued filter bank, where the imaginary part consists of sine modulated versions of the same prototype filter. Considering a real valued input signal, the output from the filter bank can be interpreted as a set of subband signals, where the real and imaginary parts are Hilbert transforms for each other. The resulting subbands are therefore analysis signals of the real valued output obtained from the cosine modulated filter bank. Therefore, due to the representation of the complex value, the subband signals are oversampled by factor two.

Synthetic filters work the same way

Is extended to.

Equations (16) and (17) mean that the output from the synthesis bank is complex-valued. Using matrix notation where Ca is a matrix with cosine modulation analysis filters from equation (13) and Sa is a matrix with sine modulation of the same factor, the filters of equation (16) are obtained with Ca + j Sa. In these matrices, k is a row index and n is a column index. Similarly, matrix Cs has the synthesis filters from equation (14), and Ss is the corresponding sine modulation version. Thus equation (17) can be written as Cs + j Ss , where k is the row index and n is the column index. If we mark the input signal as x , the output signal y is

Is confirmed.

As confirmed from equation (18), the real part includes two terms; Output from cosine modulated filter bank and output from sine modulated filter bank. If the cosine modulated filter bank has a PR attribute, its sine modulation version with a change in sign is also easily verified to constitute PR systems. Therefore, by taking the real part of the output, the complex exponential modulation system provides the same reconstruction accuracy as the corresponding cosine modulation version. That is, using a real valued input signal, the output signal of the complex exponential modulation system can be determined by taking the real part of the output signal.

The complex exponential modulation system can also be extended to process complex valued input signals. By extending the number of channels to 2M, ie by adding filters for negative frequencies, and by maintaining the imaginary part of the output signal, a pseudo QMF or PR system for complex valued signals is obtained.

It should be noted that the complex exponential modulated filter bank has only one pass band for all filters within the positive frequency range. Therefore, it is free from the main aliasing terms. The absence of main aliasing terms causes the aliasing cancellation limit from the cosine (or sine) modulation filter bank to no longer be useable in the complex exponential modulation version. Therefore, analysis and synthesis filters

And

Where A is any (possibly zero) constant, 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, i.e., reduced complexity, can be achieved.

Before providing a method for optimization of prototype filters, the disclosed methods for the design of filter banks are summarized. Based on symmetric or asymmetric prototype filters, filter banks may be generated by modulating prototype filters using, for example, a cosine function or a complex exponential function. Prototype filters for analysis and synthesis filter banks may be different or the same. When using complex exponential modulation, the main aliasing terms of the filter banks can be obsolete and eliminated, thereby reducing the aliasing sensitivity to changes in the subband signals of the resulting filter banks. Moreover, the overall system delay of the filter banks can be reduced when using asymmetric prototype filters. When using complex exponential modulated filter banks, it has also been confirmed that the output signal from the real valued input signal is determined by taking the real part of the complex output signal of the filter bank.

Next, a method for optimizing prototype filters is described in detail. If desired, the optimization increases the degree of full reconstruction, i.e. reduces the combination of aliasing and amplitude distortion, reduces sensitivity to aliasing, reduces system delay, reduces phase distortion, and / or It is aimed at reducing amplitude distortion. A first equation for the alias gain terms is determined to optimize the prototype filter p ₀ (n). In the following, the alias gain terms for the complex exponential modulated filter bank are derived. However, it should be noted that the disclosed aliasing terms are also valid for a cosine modulated (real number) filter bank.

의 실수부의 z-변환은Referring to equation (4), the output signal

The z-transformation of the real part of

는 복소 공액 시퀀스

의 z-변환이다. 식 (4)으로부터, 출력 신호의 실수부의 변환은sign

Complex conjugate sequence

Z-conversion. From equation (4), the conversion of the real part of the output signal is

Here, the input signal x (n) is a real value, that is, X * (zW ^l ) = X (zW ^-l ). (22) after rearrangement

Can be written as

Are alias gain terms used for optimization. From equation (24)

This can be observed.

In particular, for systems of real values

Which is equal to (24)

To simplify.

이

형태임이 확인될 수 있다. 더욱이, a_M/2(n)의 실수부는 영이어야, 즉

이 영이어야 하고, l ≠ 0, M/2에 대한 에일리어스 이득들이By reviewing equation (23) and recalling the transformation of equation (21), the real part of a ₀ (n) must be a Dirac pulse for the PR system, i.e.

this

Form can be confirmed. Moreover, the real part of a _{M / 2} (n) must be zero, ie

Must be zero, and the alias gains for l ≠ 0, M / 2

For a real-valued system, this means that in equation (26), all a _l (n) (l = 1 ... M-1) must be zero. In pseudo QMF systems, equation (28) is only approximately true. Moreover, the real part of a ₀ (n) is not exactly Dirac-pulse and also the real part of a _{M / 2} (n) is not exactly zero.

Before entering further details on the optimization of prototype filters, the impact of changes in subband samples on aliasing is investigated. As already mentioned above, changing the gains of the channels in the cosine modulated filter bank, i.e. using the analysis / synthesis system as an equalizer, results in severe distortion due to the main alias terms. In theory, the main aliasing terms cancel each other out in a paired manner. However, the theory of main aliasing term cancellation is not correct when different gains are applied to different subband channels. Therefore, aliasing in the output signal can be important. To illustrate this, the filter bank, i.e., channel (p) and the higher channel is set to zero gain,

Let's consider.

The formalized frequency responses of the analytical and synthesis filters of interest are shown in FIG. 2. 2 (a) shows the composite channel filters F _p-1 (z) and F _p (z), respectively, highlighted by reference numerals 201 and 202. As already mentioned above, the cosine modulation for each channel produces one positive frequency filter and one negative frequency filter. That is, positive frequency filters 201 and 202 have corresponding negative frequency filters 203 and 204, respectively.

The _p- th modulation of the analysis filter H _p-1 (z), i.e., H _p-1 (zW ^p ) indicated by the reference signs 211 and 213 is indicated by the reference signs 201 and 203. It is shown in Fig. 2 (b) with the synthesis filter F _p-1 (z). In this figure, reference numeral 211 denotes a modulated version of the original positive frequency filter H _p-1 (z) and reference numeral 213 denotes the original negative frequency filter H _p-1 (z Indicates a modulated version of)). Due to the modulation of order p, the negative frequency filter 213 is moved to the positive frequency area and thus overlaps with the positive synthesis filter 201. The shaded overlap 220 of the filters shows the energy of the main aliasing term.

In FIG. 2 (c), the p-th modulation of H _p (z), i.e., H _p (zW ^p ), denoted by reference numerals 212 and 214, is the corresponding synthesis filter ( Shown with F _p (z)). Again the negative frequency filter 214 is moved to the positive frequency area due to the modulation of order p. The shaded area 221 again shows the energy of the main alias term in the figure and will typically generate significant aliasing since it will not be erased. To eliminate aliasing, the term is a polarity inversion copy of aliasing obtained from the intersection of the filters H _p-1 (zW ^p ) 213 and F _p-1 (z) 201 of FIG. 2 (b). (polarity reversed copy), ie, a polarity reverse copy of the shaded area 220. In a cosine modulated filter bank where the gains do not change, this main aliasing terms will typically completely cancel each other out. However, in this example, the gain of the analysis (or synthesis) filter p is zero, so the aliasing induced by the filters p-1 will remain unerased in the output signal. Equally strong aliasing residuals will also appear in the negative frequency range.

When using complex exponential modulation filter banks, the modulation of the complex value results in only positive frequency filters. As a result, the main aliasing terms disappear, i.e. there is no valid overlap between the modulation analysis filters H _p (zW ^p ) and their corresponding synthesis filters F _p (z) and aliasing is _equal to the equalizers. This can be significantly reduced when using such filter bank systems. The resulting aliasing depends only on the degree of suppression of the remaining aliasing terms.

Therefore, even when using complex exponential modulated filter banks, it is important to design a prototype filter for maximum suppression of alias gain terms, even though the main aliasing terms have not been removed for such filter banks. Although the remaining aliasing terms are less important than the main aliasing terms, they can still generate aliases that cause artifacts in the processed signal. Therefore, the design of such a prototype filter can preferably be achieved by minimizing the synthesis objective function. For this purpose, various optimization algorithms can be used. Examples are for example linear programming methods, Downhill Simplex Method or non-constained gradient based method or other nonlinear optimization algorithms. In an exemplary embodiment, an initial solution of the prototype filter is selected. Using the synthesis objective function, the direction for changing the prototype filter coefficients, which provides the maximum slope of the synthesis objective function, is determined. The filter coefficients are then changed using a particular step length and the iterative procedure is repeated until the minimum value of the synthesis objective function is obtained. For further details on such optimization algorithms, see W.H. at Cambridge University Press, 1992 NY, which is incorporated herein by reference. See, "Numerical Recipes in C, The Art of Scientific Computing, Second Edition" by Press, S.A.Teukolsky, W.T.Vetterling, B.P.Flannery.

For improved alias term minimization (IATM) of the prototype filter, the desired objective function is

Where the total error e _tot (α) is the weighted sum of the transfer function error e _t and the aliasing error e _a . The first term in the unit circle, ie on the right side (RHS) of equation (23) estimated for z = e ^jω , is a measure of the error energy e _t of the transfer function.

Can be used to provide

Where P ([omega]) is a function of the symmetric real value that defines the pass band and stop band ranges, and D is the total system delay. That is, P (ω) describes the desired transfer function. In the most common case, such a transfer function includes a magnitude that is a function of frequency ω. For a system of real values, equation (31)

To be simplified.

The target function P ([omega]) and the target delay D may be selected as input parameters for the optimization procedure. The expression P (ω) e ^-jwD can be called the target transfer function.

The measure e _a of the energy of total aliasing is determined by evaluating the sum of the aliasing terms on the right side of equation (23), ie the second term of equation (23), in the unit circle.

It can be calculated as

For real valued systems, this is

Is converted to.

Overall, the optimization procedure for determining the prototype filter p ₀ (n) may be based on minimizing the error of equation (30). The parameter α can be used to distribute the emphasis between the transfer function and the sensitivity to the aliasing of the prototype filter. Increasing the parameter α to 1 further emphasizes the transfer function error e _t , and decreasing the parameter α to 0 will further emphasize the aliasing error e _a . The parameters P (ω) and D can be used to set the target transfer function of the prototype filter p ₀ (n), i.e. specify the passband and stopband operation and define the overall system delay.

According to an example, the plurality of filter bank channels k may be set to zero, for example the zero gain is provided in the upper half of the filter bank channels. As a result, the filter bank is triggered to generate a large amount of aliasing. This aliasing will subsequently be minimized by the optimization process. That is, by setting a certain number of filter bank channels to zero, aliasing can be derived to produce an aliasing error e _a , in which aliasing can be minimized during the optimization procedure. Moreover, the complexity of the calculation of the optimization process can be reduced by setting the filter bank channels to zero.

According to an example, the prototype filter is optimized for a real value, ie, cosine modulated filter bank, which may be more appropriate than directly optimizing the version of the complex value. This is because the processing of real values prioritizes aliasing attenuation far beyond the complex range. However, when triggering aliasing as described above, in this case the main part of the derived aliasing will typically originate from terms with main aliasing terms.

Therefore, the optimization algorithm can consume resources to minimize primary aliasing that is not inherent in the resulting complex exponential modulation system. To mitigate this, optimization can be done in a partial complex system; For aliasing terms that are free from main aliasing, the optimization can be done using filter processing of real values. On the other hand, the aliasing terms that will have the main aliasing terms in the real valued system will be changed for complex valued filter processing. Such partial complex optimization still optimizes the prototype filter for use in a complex modulation filter bank system, while the benefits of performing processing using real valued processing can be achieved.

In an exemplary optimization in which exactly the upper half of the filter bank channels are set to zero, the only aliasing term computed from complex valued filters is term l = M / 2 in equation (33). In this example, the function P (ω) of equation (31) covers the frequency range constituting the pass band, so that when ε is small compared to π / 2, the range is from -π / 2 + ε to π / 2- It can be chosen as a unit size constant that is ε. Outside the pass band, the function P (ω) can be defined as zero or left undefined. In the latter case, the error energy of the transfer function equation (31) is found only between -π / 2 + ε and π / 2 -ε. Alternatively or preferably, the passband error e _t can be calculated over all channels k = 0, ..., M-1, from -π to π with P (ω) constant, Aliasing, on the other hand, is still calculated with a plurality of channels set to zero as described above.

Typically the optimization procedure is an iterative procedure, where prototype filter coefficients (p ₀ (n)) (n = 0, ..., N-1), target delay (D), channels The number M, the number of low band channels set to zero (loCut), the number of high band channels set to zero (hiCut), and the weight factor α, which is a value for the objective function during this iteration step, are calculated. Using half complex operations, these steps are:

1. When P (ω) is a constant to obtain a passband error (e _t )

Find Equation (32) using

Where H _k (e ^jω ) and F _k (e ^jω ) are the analysis and synthesis filters h _k (n) and generated from the prototype filters in this iteration step from equations (13) to (15), respectively; f _k (n)).

2. to obtain an aliasing error e _a for aliasing terms for which no valid aliasing is applied;

, Where A _l (e ^jω ) is

Is calculated as

H _k (e ^jω ) and F _k (e ^jω ) are the DFT transforms, i.e., of the analysis and synthesis filters (h _k (n) and f _k (n)) from equations (13) to (15), Z-transformations from unit circles.

3. For terms to which valid aliasing applies,

은 식 (24)에 의해 제공되고, A_l(e^jω)로 식 (37)로 제공되고, H_k(e^jω) 및 F_k(e^jω)는 식 (19) 및 식 (20)으로부터의 h_k(n) 및 f_k(n)의 DFT 변환들이다.here

Is given by equation (24), A _l (e ^jω ) is given by equation (37), and H _k (e ^jω ) and F _k (e ^jω ) are obtained from equations (19) and (20) DFT transforms of h _k (n) and f _k (n).

4. The error subsequently goes to α

Weighted to

Using any of the nonlinear optimization algorithms described above, the total error is reduced by changing the coefficients of the prototype filter until an optimized set of coefficients is obtained. For example, the direction of the largest slope of the error function e _tot is determined for prototype filter coefficients in a given iteration step. Using a specific step size, the prototype filter coefficients are changed in the direction of the largest slope. The modified prototype filter coefficients are used as the starting point for subsequent iteration steps. This procedure is repeated until the optimization procedure converges to the minimum value of the error function e _tot .

An exemplary embodiment of the optimization procedure is shown by flow diagram 300 in FIG. 3. In the parameter determination step 301 the parameters of the optimization procedure, in particular the target delay (D), the number of channels (M) of the target filter bank, the number of coefficients (N) of the prototype filter, the weighting parameter of the objective error function A target transfer function is defined that includes not only? But also parameters for aliasing generation, i.e., parameters for (locut and / or hiCut). In initialization step 302, a first set of coefficients of a prototype filter is selected.

In the pass band error determination unit 303, the pass band error term e _t is determined using the provided set of coefficients of the prototype filter. This can be done using equations (35) and (32) in combination with equations (13) to (15). In the aliasing error determination unit 304 of the real value, the first portion e _aReal of the aliasing error term e _a is obtained by combining equations (36) and (37) which combine with equations (13) to (15). Can be determined using. Furthermore, in the complex valued aliasing error determination unit 305, the second portion e _aCplx of the aliasing error term e _a is to be determined using equation (38) combining equation (19) and equation (20). Can be. As a result, the objective function e _tot can be determined from the results of the units 303, 304, 305 using equation (29).

Nonlinear optimization unit 306 uses optimization methods such as linear programming to reduce the value of the objective function. For example, this can be done by determining the maximum possible slope of the objective function with respect to modifications of the coefficients of the prototype filter. That is, the changes of the coefficients of the prototype filter in which the maximum possible reduction of the objective function occurs can be determined.

If the slope determined at unit 306 remains within the predetermined boundaries, the determining unit 307 has reached the minimum value of the objective function and determines at step 308 to end the optimization procedure. On the other hand, if the slope exceeds a predetermined value, the coefficients of the prototype filter are updated in the update unit 209. The updating of the coefficients can be carried out by changing the coefficients by a predetermined step in the direction provided by the slope. Eventually, the updated coefficients of the prototype filter are inserted again as input to the passband error determination unit 303 for another iteration of the optimization procedure.

Overall, using the error function and appropriate optimization algorithm, the degree of full reconstruction of prototype filters, ie low phase and / or amplitude distortion, aliasing resilience of prototype filters by subband changes, prototype filters Prototype filters can be determined that are optimized for low aliasing related to the system delay and / or transfer function of the prototype filters. The design method is not only parameters, in particular weighting parameter (α), target delay (D), target transfer function (P (ω)), filter length (N), number of filter bank channels (M), but also aliasing trigger parameters ( HiCut, loCut), which can be selected to obtain the best combination of filter properties described above. Moreover, partial complex processing as well as setting a particular number of subband channels to zero can be used to reduce the overall complexity of the optimization procedure. As a result, asymmetric prototype filters with near complete reconstruction properties, low sensitivity to aliasing, and low system delay can be determined for use in the complex exponential modulation filter bank. It should be noted that the above decision method of the prototype filter was established in the context of a complex exponential modulated filter bank. If other filter bank design methods are used, for example cosine modulation or sine modulation filter bank design methods, the optimization procedure uses analysis and synthesis filters h _k (n) and the design equations of the respective filter bank design method. f _k (n)) can be adapted. For example, equations (13) to (15) can be used in the context of a cosine modulated filter bank.

을 제외한 모든 에일리어스 이득 항들은 실수 값의 필터들을 이용하여 계산된다. 총 시스템 지연은 D = 319로 선택되고, 프로토타입 필터 길이는 N = 640이다. 그 결과에 따른 프로토타입 필터의 시간 도메인 플롯이 도 4(a)에 제공되고, 프로토타입 필터의 주파수 응답이 도 4(b)에 도시된다. 필터 뱅크는 -72dB의 통과 대역(진폭 및 위상) 재구성 에러를 제공한다. 선형 위상으로부터의 위상 편차는 ±0.02°보다 작고, 에일리어싱 억제는 서브대역 샘플들에 변경들이 행해지지 않을 때 76dB이다. 실제 필터 계수들은 표 1에 표식화된다. 계수들은 프로토타입 필터의 절대 스케일링에 따른 본 문서에서의 다른 식들에 대해 팩터 M = 64에 의해 스케일링된다.Next, a detailed example of the 64 channel low delay filter bank is described. Using the proposed optimization method described above, a detailed example of the optimized alias gain term, low delay, 64-channel filter bank (M = 64) will be outlined. In this example, a partial complex optimization method was used and the top 40 channels were set to zero during the prototype filter optimization, ie hicut = 40, while the locut parameter remained unused. Therefore, l = 24, 40

All alias gain terms except are computed using real-valued filters. The total system delay is chosen as D = 319 and the prototype filter length is N = 640. The resulting time domain plot of the prototype filter is provided in FIG. 4 (a) and the frequency response of the prototype filter is shown in FIG. 4 (b). The filter bank provides a passband (amplitude and phase) reconstruction error of -72dB. The phase deviation from the linear phase is less than ± 0.02 ° and the aliasing suppression is 76 dB when no changes are made to the subband samples. Actual filter coefficients are labeled in Table 1. The coefficients are scaled by factor M = 64 for other equations in this document according to the absolute scaling of the prototype filter.

Although the above description of the design of the filter bank is based on the standard filter bank notation, an example for operating the designed filter bank is a filter that enables more efficient operation for other filter bank techniques or notations, for example a digital signal processor. May operate in bank implementations.

In an 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 in an efficient manner, the prototype filters from Table 1, ie p ₀ (n) are first arranged in a polyphase representation, the polyphase filter coefficients are negated one by one and all coefficients are

Flip over time

Analytical step uses vector x _l (n) of length 128

Begin with a polyphase representation of the filter being applied to the time domain signal x (n) to yield

X _l (n) is subsequently

Multiplied by a modulation matrix,

Where v _k (n), k = 0 ... 63 constitute subband signals. The time index n is consequently provided for subsequent band samples.

The complex valued subband signals are then, for example, according to some desired, possibly time varying and complex valued equalization curve g _k (n),

Can be changed as

Synthesis step

Begin with the demodulation step of the changed subband signals as

The modulation steps of equations (42) and (44) can be achieved in a very efficient manner in computation with fast algorithms using fast Fourier transform (FFT) kernels.

The demodulated samples are filtered with a polyphase representation of the prototype filter

에 축적되고,Output time domain signal according to

Accumulate in,

는 시작 시간에서 모든 n에 대해 0으로 설정된다.here

Is set to zero for all n at start time.

 It should be noted that both floating point and fixed point implementations can change the numerical accuracy of the coefficients provided in Table 1 to something more suitable for processing. Without limiting the range, the values may be rounded, truncated, and / or scaled coefficients to integers or other representations, in particular representations suitable for the available resources of the hardware and / or software platform on which the filter bank will operate. Can be quantized with lower numerical accuracy.

Moreover, the above example outlines the operation in which the time domain output signal has the same sampling frequency as the input signal. Other implementations may resample the time domain signal by using different sizes of the analysis and synthesis filter banks, for example, different numbers of channels. However, filter banks are based on the same prototype filter and are obtained by resampling the original prototype filter through abbreviation or interpolation. As an example, a prototype filter for a 32 channel filter bank may return coefficients p ₀ (n).

By resampling to.

이고, 여기서 연산자

은 자체의 인수의 정수 부분을 리턴(return)시킨다.So the new prototype filter is 320 and the delay is

Where operator

Returns the integer part of its argument.

Next, different aspects of the actual implementations are outlined. Using a standard PC or DSP, real-time operation of a low delay complex modulated filter bank is possible. The filter bank can also be hard coded on a custom chip. Fig. 5A shows the structure of an efficient implementation of the analysis part of the complex exponential modulation filter bank system. The analog input signal is first supplied to the A / D converter 501. The digital time domain signal is supplied to a shift resistor with 2M samples that shift M samples at time 502. The signals from the shift register are then filtered through the polyphase coefficients of the prototype filter 503. The filtered signals are subsequently combined 504 and simultaneously converted by the DCT-IV 505 and DST-IV 506 transforms. The outputs from the cosine and sine transforms constitute the real and imaginary parts of the subband samples, respectively. The gains of the subband samples are changed in accordance with the current spectral envelope adjuster setting 507.

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

Although the implementations described above use DCT and DST type IV transforms, implementations using DCT type II and III kernels (and also DST type II and III based implementations) are likewise possible. However, the computationally most efficient implementations for complex exponential modulation banks use pure FFT kernels. Implementations using direct matrix-vector multiplication are also possible but inferior in efficiency.

In summary, this document describes a design and method for prototype filters used in analysis / synthesis filter banks. The desired properties of the prototype filters and the resulting analysis / synthesis filter banks are nearly complete reconstruction, low delay, low sensitivity to aliasing and minimum amplitude / phase distortion. An error function is proposed that can be used in the optimization algorithm to determine the proper coefficients of the prototype filters. The error function includes a set of parameters that can be tuned to change the emphasis between desired filter attributes. Preferably, asymmetric prototype filters are used. Moreover, a prototype filter is described that provides a good compromise of the desired filter properties, namely near complete reconstruction, low delay, high resilience to aliasing and minimum phase / amplitude distortion.

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

Filter design methods and systems as well as the filter banks described herein may be implemented in software, firmware and / or hardware. Certain components may be implemented, for example, as software running on a digital signal processor or microprocessor. Other components may be implemented, for example, as hardware or as a custom semiconductor. The signals encountered in the described methods and systems may be stored in a medium such as a random access memory or an optical storage medium. They are transmitted over radio networks, satellite networks, wireless networks or wired networks, for example networks such as the Internet. Typical devices using the filter banks described in this document are set-top boxes or other customer premises equipment that decode audio signals. On the encoding side, the filter bank can be used in broadcasting stations, for example in video headend systems.

101: analysis bank 102: synthesis bank 103: analysis filter
104: decimator 105: interpolator 106: synthesis filter

Claims (11)

In the signal processing apparatus for filtering an audio signal,
A high frequency reconstructor or parametric stereo processor for producing modified complex valued subband samples;
A phase shifter for unshifting the phase of the modified complex valued subband samples by a predetermined amount; And
A composite filter bank for receiving the modified complex valued subband samples and for generating time domain output audio samples;
The synthesis filter bank is:

,

Comprises synthesis filters f _k (n) which are complex exponential modulated versions of the prototype filter p ₀ (n) according to
Where M is the number of channels, the prototype filter (p ₀ (n)) has length N, D is the system delay,
The signal processing device is at least partially implemented by one or more hardware elements. The method of claim 1,
The prototype filter (p ₀ (n)) is a symmetric low pass prototype filter or an asymmetric low pass prototype filter. The method of claim 1,
And the synthesis filter bank is a pseudo QMF bank. The method of claim 1,
And the order of the prototype filter (p ₀ (n) is equal to the system delay. The method of claim 1,
The high frequency reconstructor performs Spectral Band Replication (SBR). The method of claim 1,
And the positive value is selected to reduce the complexity of the device implementation. The method of claim 1,
The one or more hardware elements include a digital signal processor, microprocessor, or memory. The method of claim 1,
And the number of channels of the synthesis filter bank is different from the number of channels of the corresponding analysis filter bank. The method of claim 8,
And the number of channels of the analysis filter bank is 32 and the number of channels of the synthesis filter bank is 64. A method executed by a signal processing device for filtering an audio signal, the method comprising:
Generating modulated complex valued subband samples via a high frequency reconstruction process or a parametric stereo process;
Unshifting the phase of the modified complex valued subband samples by a predetermined amount; And
Filtering the modified complex valued subband samples with a synthesis filter bank to produce time domain output audio samples,
The synthesis filter bank is:

,

Comprises synthesis filters f _k (n) which are complex exponential modulated versions of the prototype filter p ₀ (n) according to
Where M is the number of channels, the prototype filter (p ₀ (n)) has length N, D is the system delay,
And the signal processing device comprises one or more hardware elements. A non-transitory computer readable medium,
A non-transitory computer readable medium comprising instructions that, when executed by a processor, perform the method of claim 10.

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