TWI716833B - Complex exponential modulated filter bank for high frequency reconstruction or parametric stereo - Google Patents

Abstract

The document relates to modulated sub-sampled digital filter banks, as well as to methods and systems for the design of such filter banks. In particular, the present document proposes a method and apparatus for the improvement of low delay modulated digital filter banks. The method employs modulation of an asymmetric low-pass prototype filter and a new method for optimizing the coefficients of this filter. Further, a specific design for a 64 channel filter bank using a prototype filter length of 640 coefficients and a system delay of 319 samples is given. The method substantially reduces artifacts due to aliasing emerging from independent modifications of 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 a digital signal processor (DSP), but can also be hardcoded on a custom chip. The method offers improvements for various types of digital equalizers, adaptive filters, multiband companders and spectral envelope adjusting filter banks used in high frequency reconstruction (HFR) or parametric stereo systems.

Description

Complex exponential modulation filter bank for high frequency reconstruction or parametric stereo

This document is about modulated sub-sampled digital filter banks, and is about the methods and systems used to design such filter banks. In particular, the present invention provides a method for reconstructing in a near-perfect manner a low delay optimized for suppression of aliasing that occurs due to modification of spectral coefficients or subband signals. Cosine or complex-exponential (complex-exponential) modulated filter bank new design method and device. In addition, a specific design of a 64-channel filter bank using a prototype filter length of 640 coefficients and a system delay of 319 samples is provided.

The disclosure of this document can be applied to: digital equalization outlined in the paper "An Efficient 20 Band Digital Audio Equalizer" published by AJSFerreira and JMNViera in AES preprint, 98 ^th Convention 1995 February 25-28 Paris, NY, USA器(digital equalizer); In the paper "Adaptive Filtering in Subbands with Critical Sampling: Analysis, Experiments, etc., published in IEEE Transaction on Signal Processing, vol. 40, no. 8, August, 1992, such as A. Gilloire and M. Vetterli "and Application to Acoustic Echo Cancellation" as outlined in "adaptive filter (adaptive filter); multi-band compander (compander); and the use of high frequency reconstruction (High Frequency Reconstruction; HFR) method of audio coding system; or An audio coding system called parametric stero technology. In the latter two examples, a digital filter bank is used for adaptive adjustment of the spectral envelope of the audio signal. An exemplary HFR system is the Spectral Band Replication (SBR) system as outlined in WO 98/57436, and the parametric stereo system as described in EP1410687.

In the entire disclosure of the present invention including the scope of the patent application, the term "subband signal" or "subband sample" means one or more output signals or one or more outputs from the analysis part of a digital filter bank Samples, or output from a forward transform (that is, the transformation of a time-domain data operation of a transform-based system). Examples of the output of such a positive conversion are from a windowed digital Fourier transform (Digital Fourier Transform; DFT) frequency domain coefficients, or from a modified discrete cosine transform (Modified Discrete Cosine Transform; MDCT) The output sample of the analysis stage.

In the entire disclosure of the present invention including the scope of the patent application, the word The term "frequency overlap" means that it is caused by decimation and interpolation, possibly combined with the modification (for example, attenuation or quantization) of the sub-band samples in the digital filter bank of the sub-fetch pattern The nonlinear distortion.

The digital filter bank is a set of digital filters composed of two or more parallel digital filters. The analysis filter bank divides the incoming signal into separate signals called sub-band signals or spectral coefficients. When the total number of subband samples per unit time is the same as the total number of input signals, the filter bank will perform critically sampled or maximum reduction. A so-called synthesis filter bank combines the equal frequency band signals into an output signal. A common type of critical pattern filter bank is a cosine modulation filter bank, in which a low-pass filter, which is a so-called prototype filter, is subjected to cosine modulation to obtain the filters. The cosine modulated filter bank provides an effective implementation and is generally used in natural audio coding systems. For further details, please refer to the paper "Introduction to Perceptual Coding" published by K. Brandenburg in AES, Collected Paperson on Digital Audio Bitrate Reduction, 1996.

A common problem with filter bank design is that any attempt to change the sub-band samples or spectral coefficients, such as by applying an equalization gain curve or quantizing the samples, will usually cause aliasing artifacts in the output signal. Therefore, it is best to have a filter bank design that can reduce such artifacts even when the subband samples are heavily modified.

One possible method is to use an oversampled (ie, non-critical sampling) filter bank. An example of superfetching pattern filter bank The sub is a category of complex exponential modulation filter bank, in which a part modulated by imaginary sine is added to the real part of a cosine modulation filter bank. EP1374399 describes such a complex index modulated filter bank, and this patent is hereby quoted for reference in the present invention.

One characteristic of complex exponential modulated filter banks is that they will not have the main aliasing terms that appear in cosine modulated filter banks. Therefore, this type of filter bank is generally less likely to have artifacts caused by the modification of the subband samples. However, there are still other aliasing terms, and the sophisticated design technology of the prototype filter of this complex exponential modulation filter bank should be implemented to eliminate the defects such as the aliasing caused by the modification of the sub-band signal. minimize. These remaining aliasing terms are usually less significant than the main aliasing terms.

A further characteristic of the filter bank is the amount of delay caused when a signal passes through the filter bank. Especially for real-time applications such as audio and video streaming, the filter or system delay should be low. One possible way to obtain a filter bank with low total system delay (ie, low delay or time delay of a signal passing through an analysis filter bank and a subsequent synthesis filter bank) is to use a short symmetric prototype filter . When a short prototype filter is used, it will usually result in poor band separation characteristics, and will result in a large frequency overlap area between adjacent sub-bands. Therefore, the short prototype filter usually does not allow the filter bank design that will appropriately suppress the frequency overlap when modifying the sub-band samples, and other methods of designing low-delay filter banks are required.

Therefore, it is best to provide a design method for filter banks that combines certain required characteristics. These characteristics are: high insensitivity to signal defects such as frequency overlap due to modification of sub-band signals; through analysis and synthesis Low delay or time delay of the signal into the filter bank; and a good approximation of perfect reconstruction characteristics. In other words, it is best to provide a method for designing a filter bank that produces a low degree of error. The sub-style filter bank usually produces two types of errors: linear distortion due to pass-band terms, and linear distortion can be further divided into amplitude and phase errors; and nonlinear distortion due to overlapping terms. Even though the "good approximation" of the Perfect Reconstruction (PR) characteristic will keep all these errors at a low level, it may be advantageous from a perceptual point of view to focus on the reduction of distortion caused by frequency overlap.

In addition, it would be better to provide a prototype filter that can be used to design an analysis and/or synthesis filter bank that exhibits these characteristics. A further required characteristic of the filter bank is to exhibit a near-fixed group delay in order to minimize artifacts due to the phase dispersion of the output signal.

This document shows that a filter bank design method called Improved Alias Term Minimization (IATM) method can be used to significantly reduce the defects caused by the phase change of the sub-band signal , In order to optimize the symmetric or asymmetric prototype filter.

This document reveals the concept of extending the design of a Quadrature Mirror Filter (Quadrature Mirror Filter; QMF for short) (that is, close to perfect reconstruction filter bank design), and covers low-latency filters using asymmetric prototype filters Group system. Therefore, it can be designed with a low system The near-perfect reconstruction filter bank is low-sensitivity to system delay, anti-frequency overlap, and/or low-level pass band error including phase dispersion. An emphasized characteristic of the filter bank characteristics can be changed according to specific requirements. Therefore, the filter bank design method according to this document alleviates the current restrictions on PR filter banks used in equalization systems or other systems that modify spectral coefficients.

The design of the low-delay complex exponential modulated filter bank according to this document can include the following steps: ‧The design is optimized for the required frequency overlap and passband error rejection and further optimized for a system delay D An asymmetric low-pass prototype filter with a cutoff frequency of π/2M; M is the number of channels in the filter bank; and ‧ Construct an M channel by applying complex exponential modulation to the optimized prototype filter Filter bank.

In addition, the operation of the low-delay complex exponential modulated filter bank according to this document may include the following steps: ‧ Filter real-valued time-domain signals through the analysis part of the filter bank; ‧ such as according to a required possibility Modification of complex-valued subband signals with time-varying equalizer settings; ‧filter the modified complex-valued subband samples through the synthesis part of the filter bank; and ‧calculate the synthesis from the filter bank The real part of the partially obtained complex-valued time-domain output signal.

In addition to proposing a new filter design method, this document also 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 disclosure of this document, especially the proposed filter bank and the filter bank designed according to the proposed design method, can be used in various applications. These applications are the improvement of various types of digital equalizers, adaptive filters, multi-band companders, and adjustments to the adaptive envelopes of filter banks used in HFR or parametric stereo systems.

According to a first point of view, a method for determining the N coefficients of the asymmetric prototype filter p ₀ used to construct the M-channel low-latency sub-pattern analysis/synthesis filter bank is explained. The analysis/synthesis filter bank may include M analysis filters h _k and M synthesis filters f _k , where k presents a value from 0 to M-1, and where M is usually greater than 1. The analysis/synthesis filter bank has an overall transfer function, and the overall transfer function is usually associated with the coefficients of the analysis and synthesis filters, and is associated with the reduction and/or interpolation operations.

The method includes the following steps: selecting a target transfer function of the filter bank that includes a target delay D. Usually choose a target delay D that is less than or equal to N. The method further includes the following steps: determining _a composite objective function e _tot which includes a passband error term e _t and a frequency stack error term e _a . The passband error term is related to the deviation between the transfer function of the filter bank and the target transfer function, and the frequency overlap error term e _a is related to the sub-sampling (that is, the reduction of the filter bank) And (or) interpolation). In a further method step, determining the asymmetric prototype filter p ₀ will reduce the N coefficients of the composite objective function e _tot .

The step of determining the target error function e _tot and the step of determining the N coefficients of the asymmetric prototype filter p ₀ are usually iteratively repeated until the minimum value of the target error function e _tot is reached. In other words, the objective function e _{tot is} determined according to a specific 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. The procedure is repeated until the target function cannot be further reduced by modifying the prototype filter coefficients. Namely means that the error function determines the target e _tot step may comprise the steps of: determining the value of a specific number of prototype composite objective function of the filter p ₀ e _tot, and the asymmetric mode of determining the prototype filter p ₀ of this step may include N coefficients of the following steps: coefficients of the prototype filter is determined p ₀ is updated in accordance with the complex of the target associated with the prototype filter p ₀ of these coefficients with a function of the gradient e _tot.

其中P(ω)e^-jωD是目標轉換函數，且

其中H_k(z)及F_k(z)分別是分析及合成濾波器h_k(n)及f_k(n)之z轉換。 According to a further point of view, the composite objective error function e _{tot is} expressed by the following formula: e _tot ( α ) = α e _t + (1- α ) e _a , where e _t is the passband error term and e _a is the frequency overlap The error term, and α is a weighting constant that exhibits values between 0 and 1. The squared deviation between the transfer function of the filter bank and the target transfer function can be accumulated for a plurality of frequencies to determine the passband error term e _t . In particular, the passband error term e _t can be calculated as follows:

Where P(ω)e ^-jωD is the objective transfer function, and

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.

其中在z=e^jω之情形下，

(z)),l=1...M-1，且其中

Accumulate the squared magnitude of each overlap gain term for a plurality of frequencies to determine the overlap error term e _a . In particular, the frequency overlap error term e _a can be calculated as follows:

Where z=e ^jω ,

(z)),l=1...M-1, and where

It is the first frequency overlap gain term estimated for the unit circle (unitcircle) with W=e ^-i2π/M , where H _k (z) and F _k (z) are the analysis and synthesis filters h _k (n) respectively And the z conversion of f _k (n). The notation A _l *(z) is the z-transformation of the complex-conjugated sequence (complex-conjugate dsequence) a _l (n).

其中n=0...N-1(針對該分析濾波器組之M個分析濾波器)；以及

其中n=0...N-1(針對該合成濾波器組組之M個合成濾波器)。 According to a further point of view, the step of determining the value of the composite objective function e _tot may include the following steps: according to the prototype filter p ₀ (n) using cosine modulation, sine modulation, and/or complex exponential modulation The analysis filter h _k (n) and the synthesis filter f _k (n) of the analysis/synthesis filter bank are generated. In particular, cosine modulation can be used to determine the analysis and synthesis filters:

Where n=0...N-1 (for M analysis filters of the analysis filter bank); and

Where n=0...N-1 (for M synthesis filters of the synthesis filter bank).

其中n=0...N-1，且A是一任意的常數(針對分析濾波器組之M個分析濾波器)；以及

其中n=0...N-1(針對合成濾波器組之M個合成濾波器)。 It is also possible to use complex exponential modulation to determine the analysis and synthesis filters as follows:

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

Where n=0...N-1 (for M synthesis filters of the synthesis filter bank).

According to another viewpoint, the step of determining the value of the composite objective function e _tot may include the following step: setting at least one filter bank channel in the filter bank channels to zero. This step can be accomplished 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 number of low frequency channels and/or a predetermined number of high frequency channels can be set to zero. In other words, the low-frequency filter bank channels (k=0 until C _low , where C _{low is} greater than zero) can be set to zero. Alternatively or additionally, the high frequency filter bank channels (k=C _high up to M-1, where C _{high is} less than M-1) can be set to zero.

In this example, the step of determining the value of the composite objective function e _tot may include the following steps: using complex exponential modulation to generate overlapping terms C _low and MC _low , and/or analysis and analysis of C _high and MC _high Synthesis filter. This step may further include the following steps: using cosine modulation to generate an analysis and synthesis filter for the residual aliasing term. In other words, the optimization procedure can be performed in a partially complex-valued manner, in which a real-valued filter (for example, a filter generated by using cosine modulation) is used to calculate the frequency overlap error term without major frequency overlap, and such as The complex index modulates the filter and modifies the frequency overlap error term that carries the main frequency overlap in the real-valued system in the complex value processing.

According to a further point of view, the analysis filter bank can use the M analysis filters h _k to generate M subband signals from an input signal. These M sub-band signals can be reduced by a factor of M to obtain the reduced sub-band signals. The downgraded sub-band signals are usually modified for purposes such as equalization or compression. The downsampled sub-band signals that may be modified can be upsampled by a factor of M, and the synthesis filter bank can use the M synthesis filters f _k to be upsampled from the upsampled The reduced sub-band signal generates an output signal.

According to another point of view, it describes a method that can be derived from the coefficients shown in Table 1 including any rounding operation, truncating operation, scaling operation, sub-sampling operation, or super-sampling operation The asymmetric prototype filter p ₀ (n) for each coefficient. Any combination of these rounding, truncation, scaling, sub-sampling, or over-sampling operations is possible.

The rounding operation of the filter coefficients can include any of the following operations: rounding to more than 20 significant digits, more than 19 significant digits, more than 18 significant digits, and more than 17 One effective digit, more than 16 effective digits, more than 15 effective digits, more than 14 effective digits, more than 13 effective digits, more than 12 effective digits, more than 11 effective digits Digits, more than 10 effective digits, more than 9 effective digits, more than 8 effective digits, more than 7 effective digits, more than 6 effective digits, more than 5 effective digits , More than 4 effective digits, more than 3 effective digits, more than 2 effective digits, more than 1 effective digit, 1 effective digit.

The truncation operation of the filter coefficients may include any of the following operations: truncation to more than 20 effective digits, more than 19 effective digits, more than 18 effective digits, and more than 17 effective digits Digits, more than 16 effective digits, more than 15 effective digits, more than 14 effective digits, more than 13 effective digits, more than 12 effective digits, more than 11 effective digits , More than 10 effective digits, more than 9 effective digits, more than 8 effective digits, more than 7 effective digits, more than 6 effective digits, More than 5 effective digits, more than 4 effective digits, more than 3 effective digits, more than 2 effective digits, more than 1 effective digit, and 1 effective digit.

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

This sub-sampling operation can include a value of 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 Sub-sampling is performed by a factor of 256. The sub-sampling operation may further include determining the sub-pattern filter coefficients as the average of the adjacent filter coefficients. In particular, the average value of the R adjacent filter coefficients can be determined as the pattern filter coefficient for this time, where R is the sub-sampling factor.

The super-sampling operation can include a value of 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 Supersampling by a factor of 10. The supersampling operation may further include determining the superfetching pattern filter coefficient as an interpolation between two adjacent filter coefficients.

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

According to another point of view, a method of generating a sub-band signal with low sensitivity to frequency overlap caused by modification of the sub-band signal is described. The method includes the following steps: determine each analysis filter of an analysis/synthesis filter bank according to the method outlined in this document; filter a real-valued time-domain signal through the analysis filters to obtain complex-valued subbands Signal; and to reduce the sub-band signals. In addition, a method for generating a real-valued output signal from a plurality of complex-valued sub-band signals with low sensitivity to the frequency overlap caused by modifying the plurality of complex-valued sub-band signals is described. The method includes the following steps: determine each synthesis filter of an analysis/synthesis filter bank according to the method outlined in this document; perform interpolation on the plurality of complex-valued subband signals; Filtering a plurality of interpolated sub-band signals; generating a complex-valued time-domain output signal that is the sum of the signals obtained from the filtering step; and obtaining the complex-valued time-domain output signal that is a real-valued output signal The real part.

According to another point of view, a system that is operable to generate sub-band signals from a time-domain input signal is described. The system includes a prototype filter that is generated according to the method outlined in this document and/or is based on it. One analyzes the filter bank.

Please note that this patent application including these methods and systems can be used alone or in conjunction with other points of view of the methods and systems disclosed in this document. Please outline the viewpoints of these methods and systems of preferred embodiments in the case. In addition, all viewpoints of the methods and systems outlined in this patent application can be combined arbitrarily. In particular, the features of the scope of patent application can be combined in any way.

101‧‧‧Analysis part

102‧‧‧Composition part

103‧‧‧Analysis filter

104‧‧‧Lower

105‧‧‧Interposer

106、201、202‧‧‧Synthesis filter

203, 204, 214‧‧‧Negative frequency filter

211, 212, 213, 214‧‧‧ Modulation of analysis filter

220, 221‧‧‧ overlap

501‧‧‧Analog to Digital Converter

502, 516‧‧‧shift register

503、515‧‧‧Prototype filter

504, 514‧‧‧ Combiner

505, 512‧‧‧ Fourth Discrete Cosine Converter

506、513‧‧‧Type 4 Discrete Sine Converter

507‧‧‧Spectrum Envelope Adjuster

511‧‧‧complex value rotation factor

517‧‧‧Digital to Analog Converter

The present invention has been described by way of example but not limiting the scope with reference to the drawings. In these drawings: Figure 1 shows the analysis and synthesis part of a digital filter bank; Figure 2 shows a set of filters The formatted frequency response of the converter is used to illustrate the adverse effects of modifying the sub-band samples in a cosine modulated (ie, real-valued) filter bank; Figure 3 is an example of an optimization procedure Flow chart; Figure 4 shows a time-domain diagram and frequency response of an optimized prototype filter for a low-delay modulated filter bank with a total system delay of 64 channels and 319 samples; and Figure 5 shows an example of the analysis and synthesis part of a low-delay complex exponential modulated filter bank system.

We should be able to understand that the disclosure of the present invention can be applied to the scope of embodiments including digital filter banks other than those explicitly mentioned in this patent. In particular, the disclosure of the present invention can be applied to other methods of designing a filter bank based on a prototype filter.

In the following, the overall transfer function of an analysis/synthesis filter bank will be determined. In other words, the mathematical representation of a signal passing through a filter bank system will be explained. The digital filter bank is a set of digital filters composed of M (M is two or more) parallel digital filters that share a common input or a common output. To know the details of this filter bank, please refer to "Multirate Systems and Filter Banks" PPVaidyanathan Prentice Hall: Englewood Cliffs, NJ, 1993. When sharing a common input, the filter bank can be called an analysis filter bank. The analysis filter bank divides the incoming signal into M separate signals called subband signals. The analysis filters are denoted as H _k (z), where k=0,...,M-1. When the sub-band signals are reduced by a factor M, the filter bank is critically sampled or reduced to the greatest extent. Therefore, the total number of subband samples per time unit across all subbands is the same as the number of samples per time unit of the input signal. The synthesis filter bank combines these sub-band signals into a common output signal. The synthesis filters are denoted as F _k (z), where k=0,...,M-1. .

Figure 1 shows a filter bank with one of M channels or sub-bands reduced to the greatest extent. The analysis part 101 generates a sub-band signal V _k (z) from the input signal X(z), and the sub-band signal V _k (z) constitutes a signal to be transmitted, stored, or modified. The synthesis section 102 recombines the signals V _k (z) into the output signal X (z).

When V _k (z) is recombined to obtain the approximate X (z) of the original signal X (z), several errors will easily occur. These errors may be due to an approximation of perfect reconstruction characteristics, and include non-linear defects due to frequency overlap, which may be caused by sub-band reduction and interpolation. Other errors that occur due to the approximation of the perfect reconstruction characteristic may be due to linear defects such as phase and amplitude distortion.

其中W=e^-i2π/M。也被稱為增加取樣單元的內插器105提供了下式所示之輸出：

且可將自合成濾波器106得到的信號之總和表示為下式：

Following the symbol shown in Figure 1, the output of the analysis filter H _k (z)103 is as follows: X _k ( z ) = H _k ( z ) X ( z ), (1) where k=0, ...,M-1. The down-sampling unit 104, also known as a down-sampling unit, provides the following output:

Where W=e ^-i2π/M . The interpolator 105, also known as the upsampling unit, provides an output shown in the following equation:

And the sum of the signals obtained from the synthesis filter 106 can be expressed as the following formula:

among them

是由被調變的輸入信號X(zW^l)與對應的頻疊增益項A_l(z)之乘積構成之M個成分的總和。可將方程式(4)改寫為下式：

Is the gain of the first overlap term X (zW ^l ). Equation (4) shows:

It is the sum of M components formed by the product of the modulated input signal X (zW ^l ) and the corresponding frequency overlap gain term A _l (z). Equation (4) can be rewritten as the following:

其中

The final sum of the Right Hand Side (RHS) constitutes the sum of all unwanted overlapping items. When canceling all the frequency overlaps, that is, using appropriate choices of H _k (z) and F _k (z) to force the sum to zero, the following equation will be obtained:

among them

滿足方程式(10)的該類型之濾波器被稱為具有完美重 建(PR)特性。如果並未完美地滿足方程式(10)，但是近似地滿足了方程式(10)，則該等濾波器屬於近似完美重建濾波器的類別。 Is the overall transfer function or distortion function. Equation (8) shows that, depending on H _k (z) and F _k (z), T(z) can be free of phase distortion and amplitude distortion. In this example, the overall transfer function will only be the delay of D samples with a fixed scale factor c, that is: T ( z ) = cz ^-D , (9) The above equation is replaced by Equation (7) yields the following equation:

This type of filter that satisfies equation (10) is said to have perfect reconstruction (PR) characteristics. If equation (10) is not perfectly satisfied, but equation (10) is approximately satisfied, the filters belong to the category of approximately perfect reconstruction filters.

In the following, a method of self-prototype filter design analysis and synthesis filter bank is explained. The resulting filter banks are called 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 symmetrical low-pass prototype filters p ₀ (n). That is, the analysis filter h _k (n) and the synthesis filter f _k (n) are respectively:

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

The aforementioned cosine modulation analysis filter bank generates real-valued subband samples of the real-valued input signal. The samples of the equal frequency band are reduced by a factor M, so that the system is critically sampled. Depending on the choice of the prototype filter, the filter bank can constitute an approximately perfect reconstruction system (that is, the so-called virtual quadrature mirror filter (QMF) bank such as that described in US5436940), or a perfect reconstruction ( PR) system. An example of the PR system is H.S. Malvar's paper "Lapped Transforms for Efficient Transform/Subband Coding" published in IEEE Trans ASSP, vol.38, no.6, 1990. Modulated Lapped Transform (MLT for short). The total delay or system delay of the traditional cosine modulated filter bank is N.

In order to obtain a filter bank system with lower system delay, this document discloses replacing the symmetric prototype filter used in the traditional filter bank with an asymmetric prototype filter. In the prior art, the design of asymmetric prototype filters has been limited to systems with perfect reconstruction (PR) characteristics. EP0874458 describes such a perfect reconstruction system using an asymmetric prototype filter. However, due to the limited freedom in designing the prototype filter, the limitation of perfect reconstruction imposes limitations on the filter bank used in, for example, equalization systems. Please note that the symmetric prototype filter has a linear phase, that is, the symmetric prototype filter has a fixed group delay in all frequencies. On the other hand, an asymmetric filter has a nonlinear phase, that is, an asymmetric filter has a group delay that can change with frequency.

In a filter bank system using asymmetric prototype filters, the analysis and synthesis filters can be expressed by the following two equations:

及

分別是長度為N_h及N_f之分析及合成原型濾波器，且D是該濾波器組系統之總延遲。在不限制範圍的情況下，下文中述及的調變式濾波器組是分析及合成原型是相同的原型之系統，亦即：

among them

and

They are the analysis and synthesis prototype filters of length N _h and N _f respectively, and D is the total delay of the filter bank system. Without limiting the scope, the modulated filter bank mentioned below is a system in which the analysis and synthesis prototypes are the same prototype, that is:

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

However, please note that when using the filter design system outlined in this document, you can decide to use different analysis and synthesis prototype filter filter banks.

)，以便 提供餘弦調變式濾波器組中之主要頻疊項之抵消。然而，於修改次頻帶樣本時，主要頻疊項的抵消被削弱，因而導致對因主要頻疊項而發生的頻疊之強烈影響。因此，最好是可完全自次頻帶樣本移除這些主要頻疊項。 An inherent characteristic of cosine modulation is that each filter has two passbands, one of which is in the positive frequency range, and a corresponding passband is in the negative frequency range. It can be proved that the so-called major or significant frequency overlap occurs due to the frequency overlap between the negative passband of the filter and the positive passband of the FM, or conversely, the frequency overlap between the positive passband of the filter and the negative passband of the FM. item. Choose the last terms in equations (13) and (14) (that is, these terms

), in order to provide the cancellation of the main aliasing terms in the cosine modulated filter bank. However, when modifying the sub-band samples, the cancellation of the main frequency overlap term is weakened, which results in a strong influence on the frequency overlap caused by the main frequency overlap term. Therefore, it is best to completely remove these major aliasing terms from the subband samples.

The so-called complex exponential modulation filter bank based on the extension of cosine modulation to complex exponential modulation can be used to remove the main aliasing terms. This extension results in an analysis filter h _k (n) expressed by the following formula:

The equation uses the same symbol as the previous one. The analysis filter can be regarded as adding an imaginary part to the real-valued filter bank, where the imaginary part contains the same prototype filter modulated by a sinusoid. Considering a real-valued input signal, the output of the filter bank can be understood as a set of sub-band signals, in which the real and imaginary parts are the Hilbert transformation of each other (Hilbert transform). The generated sub-frequency bands are thus real-valued output analysis signals obtained from the cosine modulated filter bank. Therefore, due to the complex value representation, the sub-band signal is oversampled by a factor of 2.

In the same way, the synthesis filter is extended to the following formula:

Equations (16) and (17) mean that the output of the synthesis filter bank is a complex value. When using the matrix notation, where C _a is an equation (13) one of a cosine modulated analysis filter matrix type, and S _a having the same argument (argument) is one of a sinusoidal modulation matrix, is obtained in the form of C _a + jS _a filter shown in equation (16). In these matrices, k is the row index and n is the column index. Similarly, the matrix C _s has the synthesis filter shown in equation (14), and S _s is the corresponding sine modulated matrix. Equation (17) can be expressed as C _s +jS _s , where k is the row index and n is the column index. When the input signal is expressed as x, the output signal y will be obtained from the following formula: y=(C _s +j S _s )(C _a +j S _a )x=(C _s C _a -S _s S _a )x+ j(C _s S _a +S _s C _a )x (18)

As shown in equation (18), the real part contains two items: the output from the cosine modulated filter bank and the output from a sine modulated filter bank. It is easy to prove that if a cosine modulated filter bank has perfect reconstruction characteristics, the filter bank modulated by sine whose sign is changed also constitutes a perfect reconstruction system. Therefore, by obtaining the real part of the output, the complex exponential modulation system provides the same reconstruction accuracy as the corresponding cosine modulated version. In other words, use real value input When signal, the real part of the output signal can be obtained to determine the output signal of the complex exponential modulation system.

The complex-exponential modulation system can be extended to also handle complex-valued input signals. By extending the number of channels to 2M (that is, by adding a filter for negative frequencies), and keeping the imaginary part of the output signal, a virtual quadrature image filter (QMF) for complex-valued signals is obtained Or a perfect reconstruction system.

Please note that each filter of the complex exponential modulated filter bank has only one pass band in the positive frequency range. Therefore, this filter bank has no major aliasing terms. Since there is no main frequency overlap term, the complex exponential modulated filter bank eliminates the frequency overlap cancellation limitation of the cosine (or sine) modulated filter bank. Therefore, the analysis and synthesis filter can be expressed as follows:

as well as

Where A is an arbitrary (possibly zero) constant, and as mentioned above, M is the number of channels, N is the length of the prototype filter, and D is the system delay. By using different values of A, more efficient analysis and synthesis filter bank embodiments (ie, embodiments with lower complexity) can be obtained.

Before proposing a method to optimize the prototype filter, first summarize the disclosed method of designing the filter bank. It can be based on symmetric or asymmetric prototype filters, such as using a cosine function or a complex exponential function. The type filter is modulated, thus generating a filter bank. The prototype filters used for analysis and synthesis filter banks can be different or the same. When using complex exponential modulation, the main aliasing terms of the filter banks are discarded and can be removed, thereby reducing the frequency aliasing sensitivity of the modification of the generated filter bank's sub-band signals. In addition, when using asymmetric prototype filters, the overall system delay of the filter banks can be reduced. It has also been proved that by using a complex exponential modulated filter bank, the real number part of the complex value output signal of the filter bank can be obtained to determine the output signal from a real value input signal.

In the following, a method of optimizing the prototype filter will be explained in detail. Depending on requirements, it can be used to increase the degree of perfect reconstruction (that is, reduce the combination of frequency overlap and amplitude distortion, reduce sensitivity to frequency overlap, reduce system delay, reduce phase distortion, and/or reduce amplitude distortion) The optimization is performed under the circumstances. In order to optimize the prototype filter p ₀ (n), determine the first formula of the alias gain term. In the following, the iso-fold gain term of a complex exponential modulated filter bank will be derived. However, please note that the above-mentioned iso-fold gain terms are also valid for cosine modulated (real-valued) filter banks.

的實數部分之z轉換 是：

Please refer to equation (4), output signal

The z conversion of the real part of is:

是複共軛序列

之z轉換。自方程式 (4)，將繼續下式所示的對輸出信號的實數部分之轉換：

symbol

Is a complex conjugate sequence

The z conversion. From equation (4), the conversion to the real part of the output signal will continue as shown in the following equation:

When the above formula is used, the input signal x(n) is a real value, that is, X*(zW ^l )=X(zW ^-l ). After reconfiguration, equation (22) can be expressed as the following:

among them

It is the frequency overlap gain term used in optimization. It can be seen from equation (24):

Specifically, for real-valued systems, A _Ml *( z ) = A _l ( z ) (26)

The above equation simplifies equation (24) to:

的形式為

。此外， a_M/2(n)的實數部分必須是零，亦即，

必須是零，且 對於1≠0的該等頻疊項而言，M/2必須滿足下式：A _M-l (z)=-A _l ＊(z), (28)因而對實數值系統而言，回顧方程式(26)，意指所有的a₁(n)(其中l=1...M-1)必須是零。在虛擬正交鏡像濾波器(QMF)系統中，方程式(28)只近似地適用。此外，a₀(n)的實數部分並不正好是一狄拉克脈衝，a_M/2(n)的實數部分也不正好是零。 Examining equation (23) and reviewing the transformation of equation (21), we can see that the real part of a ₀ (n) must be a Dirac pulse of a perfect reconstruction system, that is,

Is of the form

. In addition, the real part of a _M/2 (n) must be zero, that is,

Must be zero, and for such overlapping terms of 1≠0, M/2 must satisfy the following formula: A _Ml ( z )=- A _l *( z ), (28) Therefore, for real-valued systems , Recalling equation (26), it means that all a ₁ (n) (where l=1...M-1) must be zero. In the virtual quadrature mirror filter (QMF) system, equation (28) only applies approximately. In addition, the real part of a ₀ (n) is not exactly a Dirac pulse, and the real part of a _M/2 (n) is not exactly zero.

Before going into further details related to the optimization of the prototype filter, let's study the impact of modifying the subband samples for frequency overlap. As mentioned above, when the channel gains in a cosine modulated filter bank are changed, that is, when the analysis/synthesis system is used as the first equalizer, serious distortion will be caused by the main frequency overlap term. In theory, these main frequency overlap terms will cancel each other in pairs. However, when different gains are applied to different sub-band channels, the theory of the cancellation of the main aliasing terms will fail. Therefore, the frequency overlap in the output signal may be significant. In order to prove the above situation, consider that channel p and each higher channel are set to a filter bank with zero gain, which is shown in the following equation:

Figure 2 shows the formatted frequency response of the analysis and synthesis filter in question. Figure 2(a) shows the composite channel filters F _p-1 (z) and F _p (z) labeled with codes 201 and 202, respectively. As mentioned earlier, the cosine modulation for each channel will result 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.

Figure 2(b) shows the _p- th modulation of the analysis filter H _p-1 (z) (that is, H _p-1 (zW ^p ) indicated by the codes 211 and 213) and the code 201 And the synthesis filter F _p-1 (z) indicated by 203. In this figure, the code 211 indicates the original positive frequency filter H _p-1 (z) that was modulated, and the code 213 indicates the original negative frequency filter H _p-1 (z) that was modulated. Due to the modulation of the order p, the negative frequency filter 213 is moved to the positive frequency region and thus overlaps the positive synthesis filter 201. The shaded overlap area 220 of the filters shows the energy of a dominant frequency overlap term.

In Figure 2(c), the p-th modulation to H _p (z) (that is, H _p (zW ^p ) indicated by codes 212 and 214) and the corresponding corresponding with codes 202 and 204 are shown The synthesis filter F _p (z). Due to the modulation of the order p, the negative frequency filter 214 is still moved to the positive frequency region. The shaded overlap area 221 still shows the energy of a main frequency overlap term, and will usually not be able to cancel it, resulting in significant frequency overlap. In order to cancel the frequency overlap, the term should be the opposite polarity of the frequency overlap obtained by the interpolation of the filter H _p-1 (zW ^p )213 and F _p-1 (z)201 shown in Figure 2(b) Item (that is, the shaded area with the opposite polarity of the shaded area 220). In a cosine modulated filter bank whose gain does not change, these main aliasing terms will usually cancel each other completely. However, in this example, the gain of the analysis (or synthesis) filter p is zero, and the frequency overlap caused by the filter p-1 in the output signal will not be cancelled out. The same strong remnant of the overlap will occur in the negative frequency range.

When using a complex exponential modulation filter bank, the complex exponential modulation only results in a positive frequency filter. Therefore, the main aliasing term disappears, that is, there is no significant overlap between the modulated analysis filter H _p (zW ^p ) and the corresponding synthesis filter F _p (z), and when this filter is used When the device group system is used as an equalizer, it can significantly reduce the frequency overlap. The resulting aliasing depends only on the degree of suppression of the remaining aliasing terms.

Therefore, even when the complex exponential modulation filter bank is used, although the main aliasing terms have been eliminated in this filter bank, it is still very important to design a prototype filter that maximizes the aliasing gain term. of. Even though the remaining aliasing terms are less significant than the main aliasing terms, these remaining aliasing terms will still produce aliasing that will cause artifacts to the processed signal. Therefore, it is best to minimize a composite objective function and complete the design of this prototype filter. To achieve this goal, various optimization algorithms can be used. Some examples are methods such as linear programming, Downhill Simplex Method or methods based on unlimited gradients, or other nonlinear optimization algorithms. In one embodiment, a starting solution of the prototype filter is selected. When a composite objective function is used, it is determined that one of the directions that can provide the highest gradient of the composite objective function is used to modify the prototype filter coefficients. Then, a certain step length is used to modify the filter coefficients, and the iterative procedure is repeated until one of the minimum values of the composite objective function is obtained. For further details about this optimization algorithm, please refer to "Numeric RecipesinC, The Artof" by W.H.Press, S.T.Teukolsky, W.T.Vetterling, B.P. Scientific Computing, Second Edition" (Cambridge University Press, NY, 1992), the present invention hereby quotes this material for reference.

For the improved frequency overlap term minimization (IATM) of the prototype filter, a better objective function can be expressed as follows: e _tot ( α ) = α e _t + (1- α ) e _a , (30) The total error e _tot (α) is the weighted sum of the transfer function error e _t and the frequency overlap error e _a . The first term on the right-hand side (RHS) of equation (23) estimated on the unit circle (ie, for z=e ^jω ) can be used to provide the error energy e _t for the transfer function expressed by the following equation One measurement:

Where P(ω) is a symmetric real-valued function used to define the range of the pass band and stop band, and D is the total system delay. In other words, P(ω) describes the required transfer function. In the most general case, the transfer function contains the amplitude which is a function of frequency ω. For a real-valued system, equation (31) is simplified to the following equation:

The target function P(ω) and the target delay D can be selected as the input parameters of the optimization procedure. The expression P(ω)e ^-jωD can be called the objective conversion function.

The sum of the overlapping terms (ie, the second term of equation (23)) of the right-hand side (RHS) of equation (23) on the unit circle can be estimated, and the energy of the total frequency stack e _a is calculated by the following formula Measure:

For real value systems, the above equation is converted to the following equation:

In general, an optimization procedure for determining a prototype filter p ₀ (n) can be based on minimizing the error of equation (30). The parameter α can be used to assign the emphasis between the sensitivity to the transfer function and the frequency overlap of the prototype filter. When the parameter α is increased toward 1, the transfer function error e _t will be more emphasized, and when the parameter α is decreased toward 0, the frequency overlap error e _a will be more emphasized. These parameters P(ω) and D can be used to set the target transfer function of the prototype filter p ₀ (n), that is, to define the passband and cutoff characteristics and to define the overall system delay.

According to an example, some filter bank channels k can be set to zero, for example, the filter bank channels in the upper half are set to zero gain. Therefore, the filter bank is triggered to generate a large amount of frequency overlap. An optimization procedure will then be used to minimize this overlap. In other words, by setting certain filter bank channels to zero, frequency overlap will be caused, so as to generate a frequency overlap error e _a that can be minimized during the optimization process. In addition, some filter bank channels can be set to zero, thereby reducing the computational complexity of the optimization procedure.

According to an example, it is more suitable for direct comparison of complex-valued prototype filters. A prototype filter is optimized by optimizing a real value (ie, a cosine modulation type) filter bank. This is because real-value processing has higher priority than complex-value processing for the attenuation of the distant frequency overlap. However, when the frequency overlap is triggered in the manner outlined in the previous article, the main part of the induced frequency overlap in this situation will usually originate from the items carrying the main frequency overlap terms. Therefore, the optimization algorithm can use resources to minimize the main frequency overlap that does not exist in the generated complex exponential modulation system. In order to alleviate this problem, the optimization can be performed for some complex systems; real-valued filter processing can be used to perform optimization for the aliasing terms without major aliasing. On the other hand, for complex-valued filter processing, a real-valued system will be modified to carry the main aliasing terms. By using this partial complex number optimization, the benefits of performing real-value processing can be obtained, while still optimizing the prototype filter used in the complex exponential modulated filter bank system.

In the optimization that happens to set the filter bank channel in the upper half to one of zero, the only aliasing term calculated from the complex-valued filter is the l=M/2 term of equation (33). In this example, the function P(ω) of equation (31) can be selected as a unit amplitude constant ranging from -π/2+ε to π/2-ε (where ε is a fraction of π/2), In order to cover the frequency range that constitutes the passband. Outside the passband, the function P(ω) can be defined as zero, or left undefined. In the latter case, the error energy of the transfer function shown in equation (31) is estimated only from -π/2+ε to π/2-ε. Alternatively and preferably from -π to π and the P (ω) is based on the case of the lower bound of all channels constant k = 0, ..., M- 1 calculated pass band error e _t, while still as previously described The multiple channels that are set to zero calculate the frequency overlap.

其中H_k(e^jω)及F_k(e^jω)分別是在該迭代步驟中利用方程式(13)至(15)而自該等原型濾波器係數產生的分析及合成濾波器h_k(n)及f_k(n)之DFT轉換。 The optimization procedure is usually an iterative procedure, in which the prototype filter coefficient p ₀ (n) (n=0,...,N-1), target delay D, channel In the case of the number of 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 α, a value of the objective function is calculated for the iteration step. When using a semi-complex operation, the iterative procedure includes the following steps: 1. In order to obtain the passband error e _t , use the following equation and use the system as a constant P(ω) to estimate equation (32):

Where H _k (e ^jω ) and F _k (e ^jω ) are the analysis and synthesis filters h _k (n) generated from the prototype filter coefficients using equations (13) to (15) in the iteration step, respectively And the DFT conversion of f _k (n).

其中係以下式計算A_l(e^jω)：

2. In order to obtain the frequency overlap error e _a of the frequency overlap term that is not subject to significant frequency overlap, estimate the following formula:

Among them is the following formula to calculate A _l (e ^jω ):

And H _k (e ^jω ) and F _k (e ^jω ) are the DFT conversion of the analysis and synthesis filters h _k (n) and f _k (n) generated using equations (13) to (15) (that is, Estimated z-transform on the unit circle of analysis and synthesis filters h _k (n) and f _k (n)).

3. Estimate the following formula for these items subject to significant frequency overlap:

，其中A_l(e^jω)係如同方程 式(37)，且其中H_k(e^jω)及F_k(e^jω)是來自方程式(19)及(20)的h_k(n)及f_k(n)之DFT轉換。 Where equation (24) provides

, Where A _l (e ^jω ) is the same as equation (37), and where H _k (e ^jω ) and F _k (e ^jω ) are h _k (n) and f _k (from equations (19) and (20) n) DFT conversion.

4. Then the error is weighted by the following formula: e _tot ( α ) = αe _t +(1- α )( e _{a Re al} + e _aCplx ). (39)

Use any of the non-linear optimization algorithms mentioned above, and modify the prototype filter coefficients to reduce the total error until an optimal set of coefficients is obtained. For example, in a certain iteration step, the direction of the maximum gradient of the error function e _tot is determined for the prototype filter coefficients. Use a certain step size to modify the prototype filter coefficients along the direction of the maximum gradient. The modified prototype filter coefficients are used as the starting point for subsequent iteration steps. This procedure is repeated until the optimization procedure has converged to the minimum value of the error function e _tot .

Fig. 3 shows an embodiment of the optimization procedure in a flowchart 300. In a parameter determination step 301, the parameters of the optimization procedure are defined, that is, the target conversion function including the target delay D is defined in particular The number, the number of channels M of the target filter bank, the number N of prototype filter coefficients, the weighting parameter α of the target error function, and the parameters of the frequency overlap generation (ie, loCut and/or hiCut). In an initialization step 302, the first set of coefficients of the prototype filter is selected.

In the passband error determination unit 303, the passband error term e _t is determined by using the coefficients of the specific set of the prototype filter. Equation (32) can be used in conjunction with equations (35) and (13) to (15) to perform this step. In the real-valued frequency overlap error determination unit 304, equations (36) and (37) can be used in conjunction with equations (13) to (15) to determine the first part e _{aReal of the} frequency overlap error term e _a . In addition, in the complex-valued frequency overlap error determination unit 305, equation (38) can be used in conjunction with equations (19) and (20) to determine the second part e _{aCplx of the} frequency overlap error term e _a . Therefore, equation (39) can be used to determine the objective function e _tot from the results of the units 303, 304, and 305.

The nonlinear optimization unit 306 uses an optimization method such as linear programming in order to reduce the value of the objective function. For example, it is possible to determine a possible maximum gradient of the objective function in a manner related to the modification of the prototype filter coefficients, and perform this step. In other words, it is possible to determine those modifications to the prototype filter coefficients that will result in the greatest possible reduction of the objective function.

If the gradient determined in the unit 306 is still within the predetermined limit, the determination unit 307 determines that the minimization of the objective function has been reached, and the optimization procedure ends in step 308. On the other hand, if the gradient exceeds the predetermined value, the prototype filter coefficients are updated in the update unit 309. The gradient can be modified in a predetermined step in the direction provided by the gradient. Coefficients, and update these coefficients. Finally, the updated prototype filter coefficients are re-inserted as the input of the passband error determination unit 303 to perform another iteration of the optimization procedure.

In general, it can be stated as: the above-mentioned error function and a suitable optimization algorithm can be used to determine the perfect reconstruction degree for the prototype filter (that is, for the low frequency overlap combined with low phase and/or amplitude distortion The prototype filter is optimized for the adaptability of the prototype filter to the frequency overlap caused by the modification of the sub-band, the system delay of the prototype filter, and/or the conversion function of the prototype filter. The design method provides options for obtaining an optimal combination of the above-mentioned filter characteristics, especially the weighting parameter α, target delay D, target transfer function P(ω), filter length N, and number of filter bank channels. M, and some parameters of frequency overlap trigger parameters loCut and hiCut. In addition, certain number of sub-band channels can be set to zero and some complex processing can be used to reduce the overall complexity of the optimization procedure. Therefore, an asymmetric prototype filter with near-perfect reconstruction characteristics, low sensitivity to frequency overlap, and low system delay can be determined for use in a complex exponential modulated filter bank. Please note that the above-mentioned prototype filter determination system has been outlined in the context of a complex exponential modulated filter bank. If other filter bank design methods such as cosine modulation or sine modulation filter bank design methods are used, the design equations of the respective filter bank design methods can be used to generate analysis and synthesis filters h _k ( n) and f _k (n), and adjust the optimization procedure. For example, in the environment of a cosine modulated filter bank, equations (13) to (15) can be used.

In the following, a detailed example of a 64-channel low-delay filter bank will be explained. Using the above-mentioned optimization method proposed, a detailed example of a low-delay 64-channel filter bank (M=64) in which the alias gain term is optimized will be summarized. In this example, a partial complex optimization method is used, and the highest 40 channels have been set to zero during the optimization of the prototype filter, that is, hiCut=0, and the loCut parameter remains unused. Therefore, a real-valued filter is used to calculate all alias gain terms except A _l (where l=24,40). The total system delay is selected as D=319, and the prototype filter length is N=640. Figure 4(a) provides a time-domain diagram of the prototype filter generated, and Figure 4(b) shows the frequency response of the prototype filter. The filter bank provides a passband (amplitude and phase) reconstruction error of -72 dB. When no modification is performed on the subband samples, the phase deviation from a linear phase is less than ±0.02°, and the aliasing suppression is 76 decibels. Table 1 shows the actual filter coefficients. Please note that the scale of these coefficients is set with a factor of M=64 in a way that depends on the absolute scale of the prototype filter in other equations in this document.

Although the above description of the design of the filter bank is based on a standard filter bank symbol, an example of the designed filter bank can be implemented in a filter bank that can perform more efficient operations on a digital signal processor. And other filter bank descriptions or symbols.

In an example, the steps of filtering the time-domain signal using the optimized prototype filter can be described in the following way:

‧In order to operate the filter bank in an efficient manner, first configure the prototype filter in a polyphase representation (that is, p ₀ (n) in Table 1), where every other coefficient of the polyphase filter The coefficients of a polyphase filter are negative, and all coefficients change over time, as shown in the following formula:

‧At the beginning of the analysis phase, the time domain signal x(n) is applied to the multi-phase representation of the filter to generate a vector x _l (n) of length 128, as shown in the following equation:

‧Then multiply x _l (n) by a modulation matrix, as shown in the following formula:

Among them, v _k (n), k=0...63, constitute a sub-band signal. Therefore, the time index n is provided in the subband samples.

‧The complex-valued subband signals can then be modified according to some required equalization curves g _k (n) that may vary with time and are complex-valued, as shown in the following equation:

‧Start the synthesis stage by demodulating one of the modified sub-band signals, as shown in the following formula:

Please note that some fast algorithms using the Fast Fourier Transform (FFT) core can be used to complete the adjustment of equations (42) and (44) in a computationally efficient way. Change steps.

：

‧Filter the demodulated samples with the multi-phase representation of the prototype filter, and accumulate the filtered samples into the output time domain signal according to the following formula

:

對所有n被設定為0。 Where at the beginning,

For all n is set to 0.

Please note that both floating-point and fixed-point embodiments can change the numerical accuracy of the coefficients provided in Table 1 to a numerical accuracy that is more suitable for processing. Without limiting the scope, these coefficients can be rounded, truncated, and/or scaled to integers or other representations (especially hardware and/or software platforms suitable for operating the filter bank Representation of available resources), and quantify these values to a lower numerical accuracy.

In addition, the above example outlines the operation of the time domain output signal with the same sampling frequency as the input signal. Other embodiments may use analysis and synthesis filters of different sizes (that is, different numbers of channels) to resample the time domain signals. However, the filter banks should be based on the same filter bank, and the original prototype filters should be resampled through downscaling or interpolation to obtain the filter banks. For example, the same coefficient p ₀ (n) is resampled to obtain a prototype filter for a 32-channel filter bank, as shown in the following equation:

，其中算子

送回其引數的整數部分。 The length of the new prototype filter is thus 320, and the delay is

, Where the operator

Return the integer part of its argument.

In the following, some different viewpoints of the actual embodiment will be summarized. When using a standard PC or digital signal processor (DSP), real-time operation of the low-delay complex exponential modulated filter bank is feasible. The filter bank can also be hard-coded in a custom chip. Figure 5(a) shows a The structure of an effective embodiment of the analysis part of the complex exponential modulated filter bank system. First, the analog input signal is transmitted to an analog-to-digital converter 501. The digital time domain signal is transferred to a shift register 502 that stores 2M samples and shifts M samples at a time. The signal from the shift register is then filtered through the multi-phase coefficients of the prototype filter 503. The filtered signals are then combined in the combiner 504 and converted in parallel by the fourth type discrete cosine converter 505 and the fourth type discrete sine converter 506. The output from these cosine and sine converters respectively constitute the real and imaginary parts of the subband samples. The gain of the sub-band samples is modified according to the settings of the existing spectrum envelope adjuster 507.

Figure 5(b) shows an effective embodiment of the synthesis part of a low-latency complex exponential modulation system. First, multiply the equal frequency band samples by a complex-valued twiddle factor (ie, a constant dependent on the complex-valued channel) 511, and use a fourth-type discrete cosine converter 512 to modulate the real part, and use a fourth-type The discrete sine converter 513 modulates the imaginary part. The outputs of these converters are combined in the combiner 514 and transmitted through the multi-phase components of the prototype filter 515. The self-shift register 516 obtains the time-domain output signal. Finally, the time domain output signal is converted into an analog waveform in a digital-to-analog converter 517.

Although the above-mentioned embodiment uses the fourth-type discrete cosine and sine transform, the embodiment using the second-type or third-type discrete cosine transform core is also feasible (using the second-type or third-type discrete sine The same applies to the converted embodiment). However, the most computationally efficient embodiment for complex exponential modulated filter banks uses pure fast Fourier transform (FFT) core. An embodiment using direct matrix-vector multiplication is also feasible, but it is less efficient.

In summary, this document describes a prototype filter design method for analysis/synthesis filter banks. The required characteristics of the prototype filters and the resulting analysis/synthesis filter bank are near perfect reconstruction, low latency, low sensitivity to frequency overlap, and minimal amplitude/phase distortion. An error function is proposed that can be used in an optimization algorithm to determine the appropriate coefficients of the prototype filters. The error function includes a set of parameters that can be adjusted to modify the degree of emphasis between the desired characteristics. It is best to use an asymmetric prototype filter. In addition, a prototype filter that provides a good compromise with the required filter characteristics (ie, near perfect reconstruction, low delay, high adaptability to frequency overlap, and minimal phase/amplitude distortion) is described.

Although some specific embodiments and applications have been described in this specification, those who have general knowledge of this technology should understand that without departing from the scope of the invention described in this specification and claimed in the scope of the patent application, It is possible to make many changes to the embodiments and applications described in this specification. We should understand that although certain forms of the present invention have been shown and described, the present invention is not limited to the specific embodiments described and shown or the specific methods described.

The filter design method and system and filter bank described in this document can be implemented as software, firmware, and/or hardware. Certain components may be implemented as software running on a digital signal processor or microprocessor, for example. Other components can be implemented as hardware and/or application-specific integrated circuits. The signals encountered in the methods and systems mentioned can be stored in random memory such as Take media such as memory or optical storage media. These signals can be transmitted via networks such as radio networks, satellite networks, wireless networks, or wired networks such as the Internet. A typical device using the filter bank described in this document is a set-top box or other customer premise equipment that decodes audio signals. On the encoding end, these filter banks can be used in broadcast stations such as video headend systems.

Claims (10)

A signal processing device for filtering and processing audio signals. The signal processing device includes: an analysis filter bank, receiving real-valued time-domain input audio samples and generating complex-valued subband samples; a high-frequency reconstructor or parametric stereo processor, Generating modified complex-valued sub-band samples; and a synthesis filter bank, receiving the modified complex-valued sub-band samples and generating time-domain output audio samples, wherein the analysis filter bank includes an analysis filter (h _k (n)) and The synthesis filter bank includes a synthesis filter (f _k (n)) that is a complex exponential modulation version of the prototype filter (p ₀ (n)) according to the following formula:

0

n < N ,0

k < M where M is the number of channels, the prototype filter (p ₀ (n)) has length N, and the analysis filter bank and synthesis filter bank have a system delay of D samples, where D is less than N, Wherein, at least part of the signal processing device is executed by one or more hardware components. For example, the signal processing device of the first item in the scope of patent application, wherein the prototype filter (p ₀ (n)) is a symmetric low-pass prototype filter or an asymmetric low-pass prototype filter. For example, the signal processing device of item 1 in the scope of patent application, where the sub The analysis filter bank is a scalable virtual quadrature mirror filter (QMF) bank. For example, the signal processing device of the first item in the scope of patent application, wherein the order of the prototype filter (p ₀ (n)) is equal to the system delay D. For example, the signal processing device of the first item in the scope of patent application, in which the high-frequency reconstructor implements Band Copy (SBR). For example, the signal processing device of the first item of the patent application, wherein the one or more hardware components include a digital signal processor, a microprocessor, or a memory. For example, the signal processing device of the first item of the scope of patent application, wherein the number of channels in the analysis filter bank is different from the number of channels in the synthesis filter bank. For example, the number of channels in the analysis filter bank is 32, and the number of channels in the synthesis filter bank is 64 in the signal processing device of item 7 of the scope of patent application. A method implemented by a signal processing device for filtering audio signals, the method comprising: receiving real-valued time-domain input audio samples; filtering the real-valued time-domain input audio samples with an analysis filter bank to generate complex-valued subbands Samples; generate modified complex-valued subband samples through a high-frequency reconstruction program or a parametric stereo program; receive the modified complex-valued subband samples; filter the modified complex-valued subband samples with a synthesis filter bank to generate a time domain output Audio samples, where the analysis filter bank includes an analysis filter (h _k (n)) and the synthesis filter bank includes a complex exponential modulation version of the prototype filter (p ₀ (n)) according to the following formula Synthesis filter (f _k (n)):

0

n < N ,0

k < M where M is the number of channels, the prototype filter (p ₀ (n)) has length N, and the analysis filter bank and synthesis filter bank have a system delay of D samples, where D is less than N, Wherein, the signal processing device includes one or more hardware components. A non-transitory computer readable medium containing instructions when the method described in item 9 of the scope of patent application is implemented by a processor.

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