TWI772930B - Analysis filter bank and computing procedure thereof, analysis filter bank based signal processing system and procedure suitable for real-time applications - Google Patents

Abstract

An analysis filter bank corresponding to a plurality of sub-bands which performs a frequency division filtering on an input signal to generate a plurality of sub-band signals, where the sub-bands are with equal width, the analysis filter bank comprises: a sub-band response pre-compensating device which performs a linear filtering on the input signal to generate a response pre-compensating signal, a plurality of sub-filters with different central frequencies which perform a complex-type first-order infinite impulse response filtering on the response pre-compensating signal separately to generate a plurality of sub-filter signals, and a plurality of binomial combining and rotating devices based on a set of binomial weights, each performs a weighted-sum operation on at least two sub-filter signals with the set of binomial weights, and rotates the weighted-sum value with a phase according to the corresponding sub-band central frequency to generate a sub-band signal of a plurality of sub-band signals, wherein the at least two sub-filter signals are generated by at least two sub-filters of the plurality of sub-filters with adjacent central frequencies.

Description

Analysis filter bank and its operation program suitable for real-time application, based on analysis filter Signal processing system and program of wave filter group

The present invention relates to the field of acoustic wave signal processing and fundamental frequency signal processing, in particular to an analysis filter bank and its method, a real-time signal processing system based on the analysis filter bank and its implementation method.

A filter bank consists of multiple parallel filters. The parallel filters correspond to a plurality of different frequency bands respectively, which can cover the whole frequency band or part of the frequency band of the input signal of a time domain filter bank. Each of these frequency bands is called a sub-band, and the set of all the sub-bands is called a sub-band group. These parallel filters are called sub-band filters, and the output signals of the corresponding sub-bands of the filter bank (usually also the output signals of the sub-band filters) are called sub-band signals. The design of the filter bank is highly flexible: the bandwidth of each sub-band and the shape of the sub-band filter response can be adjusted independently, and the frequency responses of two sub-band filters adjacent to the center frequency can partially overlap. If the input signals of the subband filters in a filter bank are all the same input signal, the filter bank is called an analysis filter bank. For the design of the filter bank, please refer to Reference 1 to Reference 3.

When applying a filter bank in a general signal processing system, a conventional filter bank-based signal processing system architecture 100 as shown in FIG. 1 may be used. The signal processing system architecture 100 includes: an analysis filter bank 101, which filters and divides a time-domain input signal (ie, performs a plurality of filtering processes with different center frequencies to separate components of different frequencies) to obtain a plurality of subbands signal; a decimator (decimator; reducing the sampling frequency of the signal by discarding some sampling points) 102, which extracts the sub-band signals to obtain a plurality of extracted sub-band signals corresponding to each sub-band; a core digital signal processing unit 103, which performs specified signal processing on the extracted signals to obtain a plurality of modified subband signals of corresponding subbands (that is, the signal that has completed the signal processing); a zero-filling unit 104, which combines the plurality of zero values sampling points are inserted into the modified subband signals to restore the sampling frequencies of the modified subband signals to the same as the input signal; and a synthesis filter bank 105, which restores the modified subbands of the restored sampling frequencies The signals are combined into an output signal after anti-aliasing. The filter bank-based signal processing system architecture is suitable for implementing sample-based signal processing, which is more conducive to the design of low processing delay. If the signal processing system 100 is a real-type output signal such as an acoustic wave, synthesizing the output signal will typically only be performed on the real part of the modified subband signals. Also, considering that the algorithm implemented by the signal processing system 100 may need to refer to phase information, such as baseband signal processing, or some audio signal algorithms such as frequency shifting lowering), phase vocoder algorithms, etc., need to process sub-band signals of complex type (that is, with phase information), so the sub-band signals output by the analysis filter bank discussed below are all complex types. .

In terms of the architecture selection of real-time signal processing systems, in addition to the filter bank-based signal processing system architecture (hereinafter referred to as the filter bank system architecture), the analysis-modification-synthesis framework (or AMS) is based on the analysis-modification-synthesis framework (or AMS). The frequency domain signal processing system architecture (hereinafter referred to as the AMS system architecture) implemented by the framework) is also widely used in real-time signal processing applications. In this architecture, the analysis operation and the synthesis operation are in principle a pair of reversible operations, such as applying time-frequency transforms such as short-time Fourier transform (or STFT) and its inverse transform, or discrete cosine transform (discrete cosine transform) transform, or DCT) and its inverse transformation, etc. Details of waveform analysis and synthesis operations can be found in References 4 and 5. Because the frequency domain signal processing is a frame-based operation, the choice of the frame length directly affects the frequency resolution of the spectrum. If the real-time signal processing system has extremely low signal processing delay requirements, it may not be suitable for implementation with the AMS system architecture. To select an appropriate system architecture, the method is nothing more than a decision based on the system requirements, sorting and comparing several considerations. Common considerations for signal processing system architecture selection are: frequency division (decomposing the time domain waveform into signal components of different frequencies in detail), algorithm delay (the processing delay obtained by assuming that the operation time is zero, that is, the theoretical minimum processing delay), the level of computational requirements, the phase change characteristics (such as whether it is close to linear phase bit response), design flexibility (for example, whether it causes other design or parameter setting constraints), numerical stability (if there are special accuracy requirements, such as only floating-point operations) and so on. Generally speaking, if the same frequency division capability is considered (that is, the spectrum with the same resolution can be obtained), the use of filter banks to perform frequency division and waveform synthesis requires significantly higher computational requirements than using STFT conversion/inverse conversion. The computational requirements of performing frequency division and waveform synthesis, but its advantages are significantly lower algorithm delay and extremely high design flexibility (for example, it can be adjusted to any number of subbands, and the subband bandwidth and frequency can be adjusted independently. Responsive shape, while suitable for point processing or frame processing system design...etc). Therefore, seeking a filter bank design suitable for signal processing but with low computational complexity is the key for the filter bank system architecture to be suitable for real-time signal processing software implementation or very low power signal processing devices.

references

Reference 1: Wei, Ying, and Yong Lian. "A 16-band nonuniform FIR digital filterbank for hearing aid." 2006 IEEE Biomedical Circuits and Systems Conference. IEEE, 2006.

Reference 2: Subbulakshmi, N., and R. Manimegalai. "A survey of filter bank algorithms for biomedical applications." 2014 International Conference on Computer Communication and Informatics. IEEE, 2014.

Reference 3: Necciari, Thibaud, et al. "A perceptually motivated filter bank with perfect reconstruction for audio signal processing." arXiv preprint arXiv:1601.06652 (2016).

Reference 4: Dutoit, Thierry, and Ferran Marques. Applied Signal Processing: A MATLAB ^TM -based proof of concept. Springer Science & Business Media, 2010.

Reference 5: Loizou, Philipos C. Speech enhancement: theory and practice. CRC press, 2013.

In view of the relative advantages and limitations of the above-mentioned different system/algorithm architectures, the purpose of the present invention is to provide an analysis filter bank suitable for real-time signal processing and a corresponding analysis filter bank operation program, and propose a second analysis filter bank based on the analysis filter bank. A signal processing system and a corresponding signal processing program based on the analysis filter bank operation program. The analysis filter bank is based on a parallel first-order infinite impulse response (or IIR) filtering operation, with sub-band response pre-compensation and binomial combination and rotator forming the sub-bands of the analysis filter bank signal output. The analysis filter bank and the corresponding analysis filter bank operation program take into account low computational complexity, low delay and low distortion. It is quite suitable for filter bank system implementation or real-time signal processing program implementation for very low power devices.

A first aspect of the present invention provides an analysis filter bank corresponding to a plurality of sub-bands, which filters and frequency-divides an input signal according to the sub-bands to generate a plurality of sub-band signals, the sub-bands are of equal width, and the analysis The filter bank includes: a sub-band response pre-compensator, which performs a linear filtering process on the input signal to generate a response pre-compensation signal; a plurality of sub-filters with different center frequencies, which respectively make the response pre-compensation signal a complex first-order infinite impulse response filtering process to generate a plurality of sub-filtered signals; and

A plurality of binomial combinations and rotators based on a set of binomial weights, each of which performs a weighted sum operation on at least two sub-filtered signals with the set of binomial weights, and applies the result of the weighted sum operation to the corresponding sub-filter The center frequency of the band is rotated by a phase to generate a sub-band signal of the sub-band signals, wherein the at least two sub-filtered signals are generated by at least two sub-filters of the sub-filters having adjacent center frequencies.

A second aspect of the present invention provides a two-stage analysis filter bank, which includes a corresponding one of a low subband group, such as the low analysis filter bank of the first aspect, and a corresponding one of a high subband group, such as the first one. A high analysis filter bank of this aspect, the two analysis filter banks respectively perform filtering and frequency division processing on an input signal to generate a subband signal, and the subband of the low analysis filter bank responds to the linear filtering process of the precompensator Being a low-pass filtering process, the linear filtering process of the sub-band response precompensator of the high analysis filter bank is a high-pass filtering process.

A third aspect of the present invention provides a three-stage analysis filter bank, which includes one corresponding to a low subband group such as the low analysis filter bank of the first aspect, and one corresponding to a middle subband group such as the first The analysis filter bank in the aspect, and one of the corresponding high subband groups is the high analysis filter bank of the first aspect, and the three analysis filter banks respectively perform filtering and frequency division processing on an input signal to generate a plurality of subbands band signal, the subband of the low analysis filter bank The linear filtering process of the pre-compensator should be a low-pass filtering process, the linear filtering process of the sub-band response pre-compensator of the mid-analysis filter bank is a band-pass filtering process, and the high-analysis filter bank The linear filtering process of the subband response precompensator is a high-pass filtering process.

A fourth aspect of the present invention provides a filter bank system comprising:

an analysis filter bank as in the first aspect, which divides and filters an input signal to generate a plurality of subband signals;

a decimator that decimates the subband signals or their amplitudes at a decimation factor to generate an input spectrum;

a core digital signal processing unit that performs specified digital signal processing on the input spectrum to determine a plurality of subband weights corresponding to the subband signals at each time; and

A subband combiner that performs a weighted sum operation on the subband signals or their real parts with the corresponding subband weights to generate an output signal.

A fifth aspect of the present invention provides a hybrid signal processing system, which includes:

a framing and time-frequency converter, which divides an input signal into a plurality of signal frames of equal length and interval according to time, and performs a time-frequency conversion on the signal frames respectively to generate a plurality of band signals;

a plurality of analysis filter banks according to the first aspect, which respectively filter and frequency-divide the equal-band signals to generate a plurality of sub-band signals;

a decimator that decimates the subband signals or their amplitudes at a decimation factor to generate an input spectrum;

a core digital signal processing unit that performs specified signal processing on the input spectrum to determine a plurality of subband weights for a plurality of subband signals corresponding to each of the plurality of band signals;

a plurality of sub-band combiners, each of which performs a weighted sum operation on the corresponding sub-band signals of the one of the band signals with their corresponding sub-band weights to generate one of a plurality of modified band signals modified with signal; and

A frequency-to-time converter that performs a frequency-to-time conversion of the modified band signals corresponding to a plurality of sampling points at the same time to generate an output signal.

A sixth aspect of the present invention provides a filter bank operation program corresponding to a plurality of subbands, which includes the following steps:

performing a linear filtering operation on at least one sampling point of an input signal to obtain at least one sampling point corresponding to the pre-compensated signal;

performing a plurality of complex first-order infinite impulse response filtering operations with different center frequencies on the at least one sampling point of the response pre-compensated signal to obtain a plurality of sub-filtered signals, each of which includes at least one sampling point; and

A plurality of subsets corresponding to the subbands are selected from the subfiltered signals, each of which includes the same number of at least two subfiltered signals obtained by at least two filtering operations with adjacent center frequencies, and the subsets Each of the subsets corresponds to at least two sub-filtered signal sampling points at the same time to perform a weighted sum operation with a set of binomial weights, and rotate the result of the weighted sum operation by a phase with the center frequency of the corresponding sub-band to obtain a plurality of sub-bands A subband signal of the signal, which includes at least one sample point.

A seventh aspect of the present invention provides a filter bank type signal processing program, which includes the following steps:

performing a filter bank operation procedure as in the sixth aspect on at least one sampling point of an input signal to obtain a plurality of subband signals, each of which includes at least one sampling point;

If a decimation period ends, extract the sub-band signals or their amplitudes to obtain an input spectrum, execute a core signal processing procedure on the input spectrum to determine a plurality of sub-band weights corresponding to the sub-band signals, and start to calculate a a new draw cycle; and

A weighted sum operation is performed on the sub-band signals corresponding to a plurality of sampling points at the same time or their real parts with the sub-band weights to obtain at least one sampling point of an output signal.

An eighth aspect of the present invention provides a mixed signal processing program, which includes the following steps:

performing a time-frequency conversion operation on at least one signal frame of an input signal to obtain a plurality of band signals, each of which includes at least one spectral sampling point corresponding to the same frequency band;

respectively performing a filter bank operation procedure as in the sixth aspect on the band signals to obtain a plurality of subband signals, each of which includes at least one sampling point;

After a decimation period ends, the subband signals or their amplitudes are extracted to obtain an input spectrum, and a core signal processing procedure is performed on the input spectrum to determine the number of subband signals corresponding to each of the subband signals subband weights, and start to calculate a new extraction cycle;

performing a weighted sum operation on the subband signals corresponding to each of the band signals and the corresponding subband weights to obtain one modified band signal of a plurality of modified band signals, which includes at least one sampling point ;as well as

A frequency-to-time conversion operation is performed on a plurality of sample points corresponding to the same time of the modified band signals to generate a plurality of sample points of an output signal.

100: Filter Bank-Based Signal Processing System Architecture

101: Analysis Filter Banks

102: Extractor

103: Core digital signal processing unit

104: Zero filling unit

105: Synthesis Filter Banks

101: Analysis Filter Banks

201: Subband response precompensator

202: Multiple first-order IIR subfilters

203: Multiple Binomial Combinations with Spinners

700: Two-stage analysis filter bank

701: Low Analysis Filter Bank

702: High Analysis Filter Bank

703: Subband response precompensator

704: Multiple first-order IIR subfilters

705: Multiple Binomial Combinations with Spinners

706: Subband response precompensator

707: Multiple first-order IIR subfilters

708: Multiple Binomial Combinations with Spinners

800: Three-stage analysis filter bank

801: Low Analysis Filter Bank

802: Medium Analysis Filter Bank

803: High Analysis Filter Bank

804: Subband response precompensator

805: Multiple first-order IIR subfilters

806: Multiple Binomial Combinations with Spinners

807: Subband response precompensator

808: Multiple first-order IIR subfilters

809: Multiple Binomial Combinations with Spinners

810: Subband response precompensator

811: Multiple first-order IIR subfilters

812: Multiple binomial combinations with spinners

1200: Filter Bank Signal Processing System

1201: Analysis Filter Banks

1202: Extractor

1203: Core digital signal processing unit

1204: Subband Combiner

1400: Mixed Signal Processing System

1401: Framing and Time-Frequency Converters

1402: Multiple Analysis Filter Banks

1403: Extractor

1404: Core Digital Signal Processing Unit

1405: Multiple Subband Combiners

1406: Frequency-Time Converter

[FIG. 1] is a conventional filter bank-based signal processing system architecture.

[FIG. 2] is a block diagram of an analysis filter bank according to the first embodiment of the present invention.

[FIG. 3] is the frequency response diagram of the sub-band equivalent filter obtained by combining the outputs of the sub-filters with different order binomial weights according to the present invention.

[Fig. 4] is a response diagram of an example analysis filter bank using a first-order binomial combination and a rotator.

[Fig. 5] is a response diagram of an example analysis filter bank using a second-order binomial combination and a rotator.

[FIG. 6] is a flow chart of the filter bank operation procedure of the second embodiment of the present invention.

[FIG. 7] is a block diagram of a two-stage analysis filter bank according to the third embodiment of the present invention.

[FIG. 8] is a block diagram of a three-stage analysis filter bank according to the fourth embodiment of the present invention.

[Fig. 9] is a response plot of an example of a two-stage analysis filter bank using a first-order binomial combination and a rotator.

[Fig. 10] is a response plot of an example of a two-stage analysis filter bank using a first-order binomial combination and a rotator.

[Fig. 11] is a response plot of an example of a three-stage analytical filter bank using a first-order binomial combination and a rotator.

[FIG. 12] is a structural diagram of a filter bank type system according to the fifth embodiment of the present invention.

[FIG. 13] is a flow chart of the filter bank type signal processing procedure of the sixth embodiment of the present invention.

[FIG. 14] is a block diagram of a mixed signal processing system according to a seventh embodiment of the present invention.

[FIG. 15] is a flow chart of the mixed signal processing procedure of the eighth embodiment of the present invention.

In order to enable those of ordinary skill in the technical field to which the present invention pertains to further understand the present invention, preferred embodiments of the present invention are listed below, together with the accompanying drawings. The constituent content and desired effect of the present invention will be described in detail.

FIG. 2 is a block diagram of an analysis filter bank according to the first embodiment of the present invention. The analysis filter bank 101 corresponds to S subbands numbered from low to high according to the center frequency. The analysis filter bank 101 includes K parallel first-order IIR sub-filters 202, S parallel combiners and rotators based on a set of M -order binomial weights (hereinafter referred to as M -order binomial combining and rotating 203, and an optional sub-band response pre-compensator (sub-band response pre-compensator) 201. Under this structure, each sub-band signal is composed of a corresponding M -order binomial combination and a rotator of the plurality of output signals of the IIR filters (hereinafter referred to as sub-filtered signals) subsets of the set of M -order binomial The signal generated by a weighted sum operation and a phase rotation operation on the term weights. It can be equivalent to a signal generated by passing an input signal through a plurality of independent filters (hereinafter referred to as sub-band equivalent filters).

The sub-band response pre-compensator 201 is used to change the frequency response of the sub-band equivalent filters of the analysis filter bank 101, which is to perform a linear filtering process on the input signal of the analysis filter bank 101 to generate a response pre-compensated signal. The filter is a linear filter with a few non-zero fixed coefficients, which uses a small amount of operations to compensate the analysis filter bank with different configuration settings (such as the setting of the bandwidth of each sub-band, the sharing of sub-filtered signals between adjacent sub-bands) The common defects of the frequency response of these sub-band equivalent filters, such as insufficient stopband attenuation, or obvious ripples of passband gain and group delay, etc. Wait. Because the coefficients need to be adjusted with the configuration settings, Therefore, the filter formula of the subband response precompensator 201 will be described together when the embodiment of the analysis filter bank 101 is introduced in the following paragraph.

The parallel first-order IIR sub-filters 202 have different center frequencies and are numbered from low to high center frequencies. The IIR sub-filters 202 respectively perform a complex first-order IIR filtering process on the response pre-compensated signal to generate a plurality of sub-filtered signals. This filtering process can be represented by the following operations:

其中k為IIR子濾波器的編號，n為取樣時間足標，

為該響應預補償信號，y _IIR,k 為編號k子濾波信號，a _k 、b _k 分別為編號k IIR子濾波器之一複數型的反饋係數(feedback coefficient)與一實數型的前饋係數(feedforward coefficient)，其設定為：

where k is the number of the IIR sub-filter, n is the sampling time scale,

is the response pre-compensation signal, y _{IIR , k} are sub-filtered signals numbered k , a _k and b _k are a complex-type feedback coefficient (feedback coefficient) and a real-number type feedforward coefficient of one of the number k IIR sub-filters, respectively (feedforward coefficient), which is set as:

其中f _IIR,k 、BW _IIR,k 分別為編號k IIR子濾波器的中心頻率與頻寬(註)，f _SAM 為該分析濾波器輸入信號的取樣頻率。μ、ρ是適用於該等IIR子濾波器202之二可調參數，其中μ的調整目標在於讓該分析濾波器組101頻率響應的加總(以下稱為總響應)在該等子帶含蓋頻率範圍內增益維持平坦不傾斜，ρ的調整目標在於使該分析濾波器組101的總響應在該等子帶含蓋頻率範圍內增益平均值維持約0dB左右。

Where f _{IIR , k} , BW _{IIR , k} are the center frequency and bandwidth (note) of the numbered k IIR sub-filter, respectively, and f _SAM is the sampling frequency of the input signal of the analysis filter. μ and ρ are two adjustable parameters applicable to the IIR sub-filters 202, wherein the adjustment goal of μ is to make the summation of the frequency responses of the analysis filter bank 101 (hereinafter referred to as the total response) in the sub-bands including The gain in the covered frequency range is kept flat and not inclined, and the adjustment goal of ρ is to keep the average gain of the analysis filter bank 101 at about 0 dB in the covered frequency range of the subbands.

Note: The bandwidth of each of the IIR sub-filters 202 is determined by the corresponding at least one sub-band bandwidth. For example, in a design of equal width for each subband, the IIR subfilters 202 have the same bandwidth. In designs where the subband bandwidth increases with the subband center frequency, the bandwidth of each of the IIR subfilters 202 also increases with the filter center frequency.

1)二項式組合與旋轉器203之每一者將該等子濾波信號之M+1個子濾波信號以該組M階二項式權重作一加權和運算，並將該加權和運算結果隨相應子帶之中心頻率旋轉一相位以產生該等子帶信號之一子帶信號(該等子帶依中心頻率由低至高編號，故該相位可設為正比於子帶編號s)。該M+1個子濾波信號由該等IIR子濾波器202之M+1個中心頻率相鄰(即編號連續)之IIR子濾波器產生。該組M階二項式權重的編號m權重，即為(1-x) ^M 展開成多項式的第m次項係數，其可表示為： These M -orders ( M

1) Each of the binomial combination and rotator 203 performs a weighted sum operation on the M +1 sub-filtered signals of the sub-filtered signals with the set of M -order binomial weights, and the result of the weighted sum operation is changed with The center frequency of the corresponding sub-band is rotated by a phase to generate a sub-band signal of the sub-band signals (the sub-bands are numbered from low to high according to the center frequency, so the phase can be set to be proportional to the sub-band number s ). The M +1 sub-filtered signals are generated by M +1 IIR sub-filters of the IIR sub-filters 202 whose center frequencies are adjacent (ie, consecutively numbered). The number m weight of the group of M -order binomial weights is the coefficient of the mth -order term of (1- x ) ^M expanded into a polynomial, which can be expressed as:

該M階二項式組合與旋轉器203的運算如以下表示：

The operation of the M -order binomial combination and the rotator 203 is expressed as follows:

其中s為組合與旋轉器編號(即相應子帶之編號)，y _FB,s 為該分析濾波器組101的編號s子帶信號，θ為任兩中心頻率相鄰子帶(即編號相鄰子帶)之間旋轉相位的差異，其單位為弧(radian)，k _s 為該編號s之M階二項式組合與旋轉器選用的多個子濾波信號的最低編號，

為編號k _s +m子濾波信號，其餘符號同前述。

where s is the combination and rotator number (that is, the number of the corresponding sub-band), y _{FB , s} is the number s sub-band signal of the analysis filter bank 101, θ is any two adjacent sub-bands with center frequencies (that is, the numbers are adjacent to each other) The difference of the rotation phase between the sub-bands), its unit is radian, k _s is the M -order binomial combination of the number s and the lowest number of the multiple sub-filtered signals selected by the rotator,

Filter the signal for the numbered k _s + m sub, and the rest of the symbols are the same as before.

The function of formula (5) rotating the phase with the subband number is to adjust the overall response of the analysis filter bank 101 to make the subband signals approximately coherent (not cancel each other when summed), and to reduce the output signal of the analysis filter bank 101 delay. The phase difference value θ of adjacent subbands is not limited in principle, but if the value can be selected from an integer multiple of -π /2, it will make the group delay of the overall response of the analysis filter bank 101 low enough and the gain response and group delay The response fluctuations are not too severe, and the overall response can be improved without adding complex multiplication operations. The present invention adopts the setting of θ =- π /2 in the following design examples, so the phase rotation only needs the operation of real part/imaginary part exchange or sign change of the value.

Also, as mentioned above, the IIR filtering operations, weighted sum operations based on binomial weights, or phase rotation operations are all linear operations, so these operations can be freely combined or reversed in order, or even moved to this analysis. Filter pre/post. Figure 2 and the corresponding formulas (1) and (5) only represent a possible operation sequence.

The manner in which the sub-filtered signal is combined and shared with the rotator is discussed below. If these M -order binomial combinations and any two adjacent numbers of the rotator 203 share P sub-filtered signals ( P = 0, that is, each sub-filter signal is only used by one combination and rotator, not used by multiple combinations and rotators). Rotator shared), then k _s can be expressed as:

該分析濾波器組101總共需要的子濾波信號個數為K=(M-P+1)‧S+P，因共用所省下的子濾波信號佔比約為P/(M+1)。原則上，在 固定子帶信號個數與採用固定階數二項式組合與旋轉器的前提下，該等子濾波信號被共用程度越高，該分析濾波器組101所需IIR子濾波器個數越低，其總響應也越平坦，但其各子帶等效濾波器的頻率響應重疊度增加，不利於後續信號處理。故建議P選取小正整數。

The total number of sub-filtered signals required by the analysis filter bank 101 is K =( M - P +1)· S + P , and the proportion of sub-filtered signals saved by sharing is about P /( M +1). In principle, on the premise that the number of sub-band signals is fixed and a fixed-order binomial combination and rotator are used, the higher the degree of sharing of these sub-filtered signals, the more IIR sub-filters required by the analysis filter bank 101. The lower the number is, the flatter the overall response is, but the overlap of the frequency responses of the equivalent filters in each subband increases, which is not conducive to subsequent signal processing. Therefore, it is recommended to select a small positive integer for P.

1)，其作用在於強化該等子帶等效濾波器之頻率響應的止帶衰減量與過渡帶衰減斜率。圖3顯示以不同階二項式權重加權組合多個編號相鄰之子濾波信號所得之子帶等效濾波器頻率響應。由其可見一階IIR濾波響應之止帶衰減量僅在20~30dB間。經二項式權重之加權組合，相應一子帶的子帶等效濾波器頻率響應的止帶衰減量與過渡帶衰減斜率可得到一倍數(

2)提升。惟其代價是該子帶等效濾波器頻率響應與該分析濾波器組總響應的群延時也倍數提升。故其適用與否需與系統應用合併考量。實務上採一或二階二項式權重加權組合子濾波信號時，已可得到堪用的子帶等效濾波器頻率響應特性。 Using higher-order binomial combinations and rotators ( M

1), whose function is to strengthen the stopband attenuation and transition band attenuation slope of the frequency response of these subband equivalent filters. FIG. 3 shows the frequency response of the sub-band equivalent filter obtained by combining a plurality of adjacently numbered sub-filtered signals with different order binomial weights. It can be seen that the stopband attenuation of the first-order IIR filter response is only between 20 and 30 dB. Through the weighted combination of the binomial weights, the stopband attenuation and the transition band attenuation slope of the subband equivalent filter frequency response of the corresponding subband can be doubled (

2) Lift. The tradeoff is that the group delay of the subband equivalent filter frequency response and the overall response of the analysis filter bank is also multiplied. Therefore, its applicability needs to be considered in combination with the system application. In practice, when the first or second-order binomial weights are used to combine the sub-filtered signals, the frequency response characteristics of the sub-band equivalent filter can be obtained.

Next, the design of the analysis filter bank for the corresponding equal-width subbands is discussed. Since the sub-bands are of equal width, each IIR sub-filter of the analysis filter bank 101 has equal bandwidth settings, and the filter center frequencies are equally spaced on the frequency axis. The effect produced by the analysis filter bank 101 is that the sub-band equivalent filter responses (including the gain and group delay responses) are highly similar in shape to each other near the passband, and the overall response of the analysis filter bank 101 appears with frequency week period fluctuations. In order to improve the flatness of the subband equivalent filter responses and the overall response of the analysis filter bank 101, the linear filtering operation of the subband response precompensator is:

即該輸入信號與該輸入信號之一延時版本之一加權和運算。式中x為該分析濾波器組101的輸入信號，

為該子帶響應預補償器201輸出信號，D為該子帶響應預補償器201的響應長度(單位為取樣點)，BW _SB 為子帶帶寬，round為四捨五入之取整函數，C _CMP 為實數型態參數，其餘符號同前述。參數C _CMP 的調整目標在於抵消C _CMP =0(即該子帶響應預補償器201未作用)時該分析濾波器組101的總響應的增益與群延時波動。另外，該等IIR子濾波器202具相同頻寬，因此b _k 值也相同，可移出濾波器公式(如併入子帶響應預補償器)以再減少該等IIR子濾波器202之運算量。

That is, the input signal is a weighted sum operation with a delayed version of the input signal. where x is the input signal of the analysis filter bank 101,

is the output signal of the sub-band response pre-compensator 201, D is the response length of the sub-band response pre-compensator 201 (unit is sampling point), BW _SB is the sub-band bandwidth, round is the rounding function of rounding, C _CMP is Real number type parameter, other symbols are the same as above. The adjustment goal of the parameter C _CMP is to cancel the gain and group delay fluctuation of the overall response of the analysis filter bank 101 when C _CMP =0 (ie, the sub-band response precompensator 201 is not active). In addition, the IIR sub-filters 202 have the same bandwidth, so the value of b _k is also the same. The filter formula can be removed (eg, a sub-band response precompensator is incorporated) to further reduce the computational complexity of the IIR sub-filters 202 .

Figure 4 shows the response of an analytical filterbank design example using a first-order binomial combination and a rotator (the solid line in the figure is the subband equivalent filter response, the dashed line is the overall response of the analytical filterbank, the dots line is the total response obtained by increasing the weight of the subband signal on its high frequency side). The sampling frequency of the input signal of the analysis filter bank is 12kHz, which is divided into 18 equal-width subbands from zero frequency (DC) to the Nyquist frequency (half the sampling frequency, which is also the highest frequency of the digital audio), so each subband The bandwidth is 333Hz. The analysis filter bank 101 requires 19 first-order IIR sub-filters, each sub-band signal consists of two sub-filtered signals, and the The center frequency of the two IIR sub-filters with the same bandwidth and the same center frequency is located at the boundary between the sub-band and the adjacent two sub-bands.

Figure 5 shows the response of an analytical filterbank design example using a second-order binomial combination and a rotator (the solid line is the subband equivalent filter response, the dashed line is the overall response of the analytical filterbank, the dotted line total response to increase the weight of its high-frequency side subband signal). The sampling frequency and sub-band definition (number of sub-bands, frequency range/bandwidth of sub-bands) of the input signal of the analysis filter bank are the same as in the previous example. The analysis filter bank requires 37 first-order IIR sub-filters, and each sub-band signal is composed of three sub-filtered signals. The center frequency of the IIR subfilter is at the center of this subband. For clarity of illustration, these two examples use filter bank settings with fewer subbands. The number of filter bank subbands in practical application will be more.

As can be seen from the figure, the subband equivalent filters of the analysis filter bank using the second-order binomial combination and the rotator in these two examples have a gain response transition band compared with the first-order binomial combination and the rotator. The version of the analysis filter bank is steeper and has a slightly wider/flater response passband. However, the cost of obtaining this better response characteristic is about twice the number of complex multiplications and about twice the filter group delay. In addition, regardless of the first- or second-order binomial combination and rotator example, the overall response (including gain response and group delay response) of the two-analytical filter bank is generally flat, maintaining a near-linear phase characteristic (Note). The sum of the impulse responses of all subbands of the two-analysis filter bank (ie, the overall impulse response) is an impulse with almost no linear distortion. Exciter function, that is, without providing additional gain to each sub-band signal, the sum of the sub-band signals is like the input waveform delayed for a small period of time. However, the higher-order binomial combination filter bank system response is more sensitive to the adjustment of subband weights, and the fluctuation of the total response (including gain and group delay) is also more obvious.

Note: However, the frequency response of the equivalent filter of individual subbands is not flat, it does not have linear phase characteristics, and its group delay may also be higher than the group delay of the total response of the analysis filter bank.

In practice, the analysis filter bank of first or second order binomial combination and rotator is used, and its sub-band equivalent filter can already obtain good stop-band attenuation and transition-band attenuation slope. The advantage of using a higher-order binomial combination and rotator is that the sub-band equivalent filter can obtain a higher stop-band attenuation and transition-band attenuation slope (each increase of one order, about 20dB to 30dB more stopband attenuation can be obtained ), and make the subband equivalent filter have a relatively flat passband response. But the cost is: 1) the ratio of these sub-filtered signals shared by multiple combiners decreases, and the overall computation amount also increases with the binomial combination and the order of the rotator; 2) these sub-band equivalent filters are the same as the The group delay of the overall response of the analysis filter bank also increases with the order of the combiner, and 3) the weighting of the subbands by the signal processing algorithm will result in more pronounced group delay response fluctuations in the overall response. Therefore, unless the need for stopband attenuation is extremely high, it is recommended to use first or second order binomial combinations and rotators in preference to designing this analysis filter bank.

The analysis filter bank 101 can be adjusted to the configuration of corresponding unequal width subbands, which are commonly used in audio processing. In short, human hearing has a structure of filtering and frequency division, which is generally called for the auditory filter. The normal auditory filter has a wider frequency performance for the higher frequency signal, while the corresponding filter bandwidth of the lower frequency signal remains roughly unchanged. This filtering bandwidth is often referred to as the critical band width. Therefore, the filter bank of the audio processing system in the literature is often designed to be similar to the configuration of the auditory filter, that is, a narrow-band sub-band filter with equal bandwidth is arranged at low frequencies (such as 500 Hz or below), and the higher the frequency, the higher the frequency. Configure the subband filter with wider bandwidth. The aforementioned filter bank design formulas (1) to (6) are still applicable in the configuration of unequal width subbands. Things to keep in mind when designing:

- In the configuration of equal-width sub-bands, the IIR sub-filters 202 can be designed to have equal bandwidths and their center frequencies are equally spaced on the frequency axis, so that the filtering formula can be simplified (because the values of b and _k are all equal) , can be removed from the filter formula (1) ~ if the input signal is first multiplied by b _k before entering the analysis filter bank 101). However, it cannot be simplified in the same way when using an analysis filter bank of corresponding unequal width subbands.

- In the configuration of unequal width sub-bands, the sub-band response pre-compensator 201 cannot effectively compensate the response, at this time, the function of the sub-band response pre-compensator 201 can be stopped (for example, set C _CMP =0, or use the input signal as the IIR sub-filters 202 input) and instead increase the IIR sub-filter bandwidth to suppress fluctuations in the overall response (including gain response and group delay response) of the analysis filter bank 101, at the cost of a small increase The transition band width of the frequency responses of the subband equivalent filters.

In addition to being implemented in a physical device, the function of the analysis filter bank 101 can also be Implemented with an equivalent program executing on at least one processor. FIG. 6 is a flow chart of a filter bank operation procedure according to the second embodiment of the present invention. The filter bank operation procedure corresponds to a plurality of subbands, which are numbered from low to high according to the center frequency. These flow steps focus on the processing method for a segment of a continuous input audio. Therefore, in real-time audio processing applications, each step performs a segmental operation on the signal; the latter steps can use the previous steps to obtain an output signal. Fragments are taken as input and computed immediately, without waiting for the full output signal from previous steps. The following formulas (1) to (7) and their corresponding descriptions are referred to when describing the flow steps of the filter bank operation procedure.

In FIG. 6, a linear filtering operation is performed on at least one sampling point of an input signal to obtain at least one sampling point corresponding to the pre-compensated signal (step S101). Referring to the descriptions of paragraphs [0017] and [0024], the linear filtering operation corresponds to the operation of formula (7), and its function is to make the frequency response of the sub-band equivalent filter flatter, and to offset the gain and group delay fluctuations of the total response .

A plurality of complex first-order IIR filtering operations with different center frequencies are performed on the at least one sampling point of the response pre-compensated signal to obtain a plurality of sub-filtered signals (step S102). Referring to the description in paragraph [0018], these complex first-order IIR filtering operations correspond to the operations of formulas (1) to (3). Each of the sub-filtered signals includes at least one sample point.

A plurality of subsets corresponding to the subbands are selected from the subfiltered signals, each of which includes the same number of at least two subfiltered signals obtained by at least two filtering operations with adjacent center frequencies, and the subsets Each of the subsets corresponds to at least two sub-filtered signal sampling points at the same time to perform a weighted sum operation with a set of binomial weights, and rotate the result of the weighted sum operation by a phase with the center frequency of the corresponding subband to obtain a plurality of subbands. A sub-band signal of the band signal (step S103), which includes at least one sampling point. Referring to the description of paragraph [0019], the binomial weight corresponds to the formula (4), the weighted sum operation and the rotation operation correspond to the operation of the formula (5). With reference to the description of paragraph [0020], the adjacent subband phase difference value θ adopts an integer multiple of -π /2, so when the rotation operation is performed for the two sub-filtered signal subsets of the adjacent sub-bands of the corresponding two frequencies, the corresponding The difference between the two rotational phases is an integer multiple of -π /2 arcs. In addition, referring to the description in paragraph [0022], two adjacent combinations and rotators can share sub-filtered signals, so the two sub-filtered signal subsets corresponding to two adjacent frequency subbands have the same sub-filtered signals.

The analysis filter bank 101 has a weakness in the configuration of the corresponding unequal width subbands: in audio processing applications, the high frequency subbands are usually much wider than the lower frequency subbands. If combined with a lower-order binomial combination and a rotator, the sub-band equivalent filter with a higher center frequency of the analysis filter bank 101 may have problems such as too wide transition band/insufficient stopband suppression (eg, lower than 40dB). , which may affect the performance of some signal processing algorithms.

To solve this problem, a third embodiment of the present invention proposes a two-stage analysis filter bank 700, which is formed by combining two parallel analysis filter banks, as shown in FIG. 7 . The two analysis filter banks are a low analysis filter bank 701 and a high analysis filter bank 702 . A low sub-band group and a high sub-band group corresponding to the two analysis filter groups 701 and 702 respectively, and their covered frequency bands are separated by a boundary frequency f _BND . The low sub-band group has SL _sub -bands whose center frequencies are all lower than f _BND . The high sub-band group has SH _sub -bands whose center frequencies are not lower than f _BND (Note). Each of the two subband groups can be respectively set as non-equal-width, equal-width, or partially equal-width subband groups. The two analysis filter banks 701 and 702 respectively perform filtering and frequency division processing on an input signal to generate a plurality of subband signals.

Note: The boundary frequency f _BND should be set so that the high sub-band group contains the high-frequency sub-band whose bandwidth is too wide to make the sub-band equivalent filter respond to the low-frequency side of the stop-band suppression ability, and it is expected that the compensation for hearing loss may be affected by the high frequency sub-band. Mid-to-high frequency subbands with substantially increased subband signal gain

To make the overall response of the two-stage analysis filter bank 700 (including gain and group delay responses) smooth without breakpoints at the crossover frequency, the following design constraints are added:

- the combiners of each of the two analysis filter banks 701, 702 are M -order binomial combiners and rotators, and any two adjacent combiners with numbers share P sub-filtered signals.

- The phase difference of the two subband response precompensators 703 and 706 in response to each frequency is a fixed value that is an integer multiple of π /2 (to achieve this effect, the two subband response precompensators can use the same group delay linear phase filter). In this way, the boundary frequency f _BND can be freely set without increasing the phase rotation computation amount of the combiners 705 and 708 .

- the highest center frequency IIR sub-filter of the low analysis filter bank 701 and the lowest center frequency IIR sub filter of the high analysis filter bank 702 have the same center frequency and bandwidth, that is:

其中K _L 為該低分析濾波器組701的IIR子濾波器個數，

、

分別為該低分析濾波器組701之編號K _L IIR子濾波器的中心頻率與頻寬，f _HIIR,1、BW _HIIR,1分別為該高分析濾波器組702之編號1 IIR子濾波器的中心頻率與頻寬。

Wherein KL is the number of _IIR sub-filters of the low analysis filter bank 701,

,

are respectively the center frequency and bandwidth of the number K _L IIR sub-filter of the low analysis filter bank 701 , f _{HIIR ,1} , BW _{HIIR ,1} are respectively the number 1 IIR sub filter of the high analysis filter bank 702 Center frequency and bandwidth.

In the low analysis filter bank 701 , the linear filtering operation of the subband response precompensator 703 is a low pass filtering operation to increase the out-of-band height of each subband equivalent filter of the low analysis filter bank 701 frequency suppression, the low-pass filtering operation can be expressed as:

其中

為該子帶響應預補償器703輸出信號，其餘符號同前述。為搭配公式(9)之該子帶響應預補償器703之運算，該等IIR子濾波器704的b _k 設定改為：

in

Responding to the precompensator 703 output signal for this subband, the rest of the symbols are the same as described above. To match the operation of the subband response precompensator 703 of equation (9), the b _k settings of the IIR subfilters 704 are changed to:

其中f _LIIR,k 、BW _LIIR,k 分別為該低分析濾波器組701之編號k IIR子濾波器之中心頻率與頻寬，其餘符號皆同前述。該等IIR子濾波器704依公式(1)(2)(10)運算(式中

以

代入)，該低分析濾波器組701之 該等子帶信號則依公式(4)~(6)運算(式中s範圍介於[1,S _L ]間)。該低分析濾波器組701的子帶信號，即該二段式分析濾波器組700同編號的子帶信號。

Wherein f _{LIIR , k} , BW _{LIIR , k} are respectively the center frequency and bandwidth of the number k IIR sub-filter of the low analysis filter bank 701 , and other symbols are the same as those described above. The IIR sub-filters 704 operate according to equations (1)(2)(10) (where

by

Substitute), the subband signals of the low analysis filter bank 701 are calculated according to formulas (4) to (6) (where s ranges between [1, S _L ]). The subband signal of the low analysis filter bank 701 is the subband signal of the same number of the two-stage analysis filter bank 700 .

In the high analysis filter bank 702 , the linear filtering operation of the subband response precompensator 706 is a high pass filtering operation to increase the out-of-band low frequency rejection of the subband equivalent filters of the high analysis filter bank 702 . The high-pass filtering operation can be expressed as:

其中

為該子帶響應預補償器706輸出信號，其餘符號同前述。為搭配公式(11)之該子帶響應預補償器706之運算，該等IIR子濾波器707的b _k 設定改為：

in

Responding to the precompensator 706 output signal for this subband, the remaining symbols are the same as described above. To match the operation of the subband response precompensator 706 of Equation (11), the b _k settings of the IIR subfilters 707 are changed to:

其中f _HIIR,k 、BW _HIIR,k 分別為該高分析濾波器組702之編號k IIR子濾波器之中心頻率與頻寬，其餘符號皆同前述。該等IIR子濾波器707依公式(1)(2)(12)運算(式中

以

代入)。該高分析濾波器組702的編號s子帶信號即該兩段式分析濾波器組700的編號S _L +s子帶信號，其可表示為：

Wherein f _{HIIR , k} , BW _{HIIR , k} are the center frequency and bandwidth of the number k IIR sub-filter of the high analysis filter bank 702 , respectively, and other symbols are the same as above. The IIR sub-filters 707 operate according to formulas (1) (2) (12) (where

by

substitute). The number s subband signal of the high analysis filter bank 702 is the number SL + s _subband signal of the two-stage analysis filter bank 700, which can be expressed as:

其中φ _H,s 為編號s子帶信號的相位旋轉量，k _s 為該高分析濾波器組702 之編號s組合器選用的多個子濾波信號之最低編號，

為該高分析濾波器組702之編號k _s +m子濾波信號，

為該兩段式分析濾波器700之編號S _L +s子帶信號，其餘符號同前描述。B _M,m 與k _s 分別依公式(4)(6)計算(式中s範圍介於[1,S _H ]間)。

where φ _{H , s} is the phase rotation amount of the sub-band signal numbered s , k _s is the lowest number of a plurality of sub-filtered signals selected by the number s combiner of the high analysis filter bank 702,

filter the signal for the number ks ₊ m sub-filters of the high analysis filter bank 702,

For the numbered SL + s _subband signal of the two-stage analysis filter 700, the rest of the symbols are the same as described above. B _{M , m} and k _s are calculated according to formulas (4) and (6) respectively (where the range of s is between [1, S _H ]).

In addition to being implemented by a physical device, the functions of the two-stage analysis filter bank 700 can also be implemented by a two-stage filter bank operation program executed on at least one processor. The two-stage filter bank operation program respectively executes two filter bank operation procedures of corresponding two subband groups on at least one sampling point of an input signal to obtain a plurality of subband signals. For the definition of the two subband groups, refer to the description in paragraph [0035]. Refer to the descriptions of paragraphs [0030]~[0033] for the operation procedure of the two-stage filter bank, and match the setting and calculation formula of the two-stage analysis filter bank (refer to the descriptions of paragraphs [0036]~[0038]). Each of the subband signals includes at least one sample point.

In the above-mentioned design of the two-stage analysis filter bank 700 , the two analysis filter banks 701 and 702 only strengthen the stopband suppression capability of one side of each subband equivalent filter. If the number of sub-bands to be considered is small and each sub-band generally has a wider bandwidth, the sub-band equivalent filter of the corresponding mid-band frequency may still face the problem of insufficient suppression in the stop-bands on both sides of the high/low frequency response of the corresponding mid-band frequency. Therefore, the fourth embodiment of the present invention provides a three-stage analysis filter bank 800, which is composed of three parallel analysis filter banks.

FIG. 8 is a block diagram of the three analysis filter banks, which include a low analysis filter bank 801 , a medium analysis filter bank 802 , and a high analysis filter bank 803 . A low subband group, a neutron subband group, and a high subband group corresponding to the three analysis filter groups respectively, and their covered frequency bands are separated by a low boundary frequency f _BNDL and a high boundary frequency f _BNDH . The low subband group has SL _subbands whose center frequencies are all lower than the low boundary frequency f _BNDL , and the neutron subband group has SM _subbands whose center frequencies are all between the low boundary frequency f _BNDL to the high Between the junction frequencies f _BNDH , the high sub-band group has SH sub-bands, and the center frequencies of which _are all higher than the high junction frequency f _BNDH . Each of the three subband groups can be configured as a non-equal width, equal width, or partial equal width subband group. The three analysis filter banks 801 , 802 and 803 respectively perform filtering and frequency division processing on an input signal to generate a plurality of subband signals.

In order to make the overall response of the three-stage analysis filter bank 800 (including gain and group delay response) smooth without breakpoints at the two boundary frequencies, the following design constraints are added:

- The combiners of each of the three analysis filter banks 801, 802, 803 are M -order binomial combiners and rotators, and any two adjacent combiners with numbers share P sub-filtered signals.

- The two sub-band response pre-compensators 804, 807 have a fixed value whose phase difference is an integer multiple of π /2 in response to each frequency, and the two sub-band response pre-compensators 807, 810 are in a frequency response to each frequency The phase difference is also a fixed value of an integer multiple of π /2 (to achieve this effect, the three-subband response precompensator can use a linear phase filter with the same group delay). In this way, the two boundary frequencies f _BNDL and f _BNDH can be freely set without increasing the phase rotation computation amount of the combiners 806 , 809 and 812 .

- the highest center frequency IIR subfilter in the low analysis filter bank 801 and the lowest center frequency IIR subfilter in the middle analysis filter bank 802 have the same center frequency and bandwidth, and the middle analysis filter bank 802 has the same center frequency and bandwidth The highest center frequency IIR sub-filter of and the lowest center frequency IIR sub-filter in the high analysis filter bank 803 have the same center frequency and bandwidth, that is:

其中K _L 、K _M 分別為該低分析濾波器組801與該中分析濾波器組802的IIR子濾波器個數，

、

分別為該低分析濾波器組801之編號K _L IIR子濾波器的中心頻率與頻寬，f _MIIR,1、BW _MIIR,1分別為該中分析濾波器組802之編號1 IIR子濾波器的中心頻率與頻寬，

、

分別為該中分析濾波器組802之編號K _M IIR子濾波器的中心頻率與頻寬，f _HIIR,1、BW _HIIR,1分別為該高分析濾波器組803之編號1 IIR子濾波器的中心頻率與頻寬。

_Wherein KL and KM are respectively the number of _IIR sub-filters of the low analysis filter bank 801 and the middle analysis filter bank 802,

,

are respectively the center frequency and bandwidth of the number K _L IIR sub-filter of the low analysis filter bank 801 , f _{MIIR ,1} and BW _{MIIR ,1} are respectively the number 1 IIR sub filter of the middle analysis filter bank 802 . Center frequency and bandwidth,

,

are the center frequency and bandwidth of the K _M IIR sub-filter of the middle analysis filter bank 802 respectively, f _{HIIR ,1} , BW _{HIIR ,1} are the number 1 IIR sub-filter of the high analysis filter bank 803 respectively Center frequency and bandwidth.

The linear filtering operation of the subband response precompensator of the low analysis filter bank 801 is a low pass filtering operation to increase the out-of-band high frequency rejection of the subband equivalent filters of the low analysis filter bank 801 . The sub-band response pre-compensation of the analysis filter bank 802 The linear filtering operation of the filter is a bandpass filtering operation to simultaneously increase the out-of-band low frequency and high frequency rejection of each sub-band equivalent filter of the mid-analysis filter bank 802 . The linear filtering operation of the subband response precompensator of the high analysis filter bank 803 is a high pass filtering operation to increase the out-of-band low frequency rejection of the subband equivalent filters of the high analysis filter bank 803 . The filtering operations of the three-subband response precompensator can be expressed as:

其中

為該低分析濾波器組801之該子帶響應預補償器804的輸出信號，

為該中分析濾波器組802之該子帶響應預補償器807的輸出信號，

為該高分析濾波器組803之該子帶響應預補償器810的輸出信號，其餘符號同前述。

in

for the subband of the low analysis filter bank 801 to respond to the output signal of the precompensator 804,

is the output signal of the precompensator 807 for the subband of the analysis filter bank 802,

The subbands of the high analysis filter bank 803 are in response to the output signal of the precompensator 810, and the rest of the symbols are the same as described above.

In the low analysis filter bank 801, in order to match the operation of the subband response precompensator 804 in equation (17), the b _k settings of the IIR subfilters 805 are changed to:

其中f _LIIR,k 、BW _LIIR,k 分別為該低分析濾波器組801之編號k IIR子濾波器之中心頻率與頻寬，其餘符號皆同前述。該等IIR子濾波器805依公式(1)(2)(20)運算(式中

以

代入)，該等子帶信號則依公式(4)~(6)運算(式中s範圍介於[1,S _L ]間)。該低分析濾波器組801的子帶信號，即該三段式分析濾波器組800同編號的子帶信號。

Wherein f _{LIIR , k} , BW _{LIIR , k} are respectively the center frequency and bandwidth of the number k IIR sub-filter of the low analysis filter bank 801 , and other symbols are the same as above. The IIR sub-filters 805 operate according to formulas (1) (2) (20) (where

by

Substitute into), these sub-band signals are calculated according to formulas (4)~(6) (where s ranges between [1, S _L ]). The subband signals of the low analysis filter bank 801 are the subband signals of the same number of the three-stage analysis filter bank 800 .

In the middle analysis filter bank 802, in order to match the operation of the subband response precompensator 807 in formula (18), the b _k settings of the IIR subfilters 808 are changed to:

其中f _MIIR,k 、BW _MIIR,k 分別為該中分析濾波器組802之編號k IIR子濾波器之中心頻率與頻寬，其餘符號皆同前述。該等IIR子濾波器808依公式(1)(2)(21)運算(式中

以

代入)。該中分析濾波器組802的編號s子帶信號即該三段式分析濾波器組800的編號S _L +s子帶信號，其可表示為：

Wherein f _{MIIR , k} , BW _{MIIR , k} are the center frequency and bandwidth of the sub-filter k IIR of the middle analysis filter bank 802 , respectively, and other symbols are the same as above. The IIR sub-filters 808 operate according to equations (1)(2)(21) (where

by

substitute). The number s subband signal of the middle analysis filter bank 802 is the number SL + s _subband signal of the three-stage analysis filter bank 800, which can be expressed as:

其中φ _M,s 為該中分析濾波器組802之編號s子帶信號的相位旋轉量，k _s 為該中分析濾波器組802之編號s組合器選用的多個子濾波信號之最低編號，

為該中分析濾波器組802之編號k _s +m子濾波信號，

為該三段式分析濾波器800之編號S _L +s子帶信號，其餘符號同前描述。B _M,m 與k _s 分別依公式(4)(6)計算(式中s範圍介於[1,S _M ]間)。

Where φ _{M , s} is the phase rotation amount of the sub-band signal of the number s of the middle analysis filter bank 802, k _s is the lowest number of the multiple sub-filter signals selected by the number s combiner of the middle analysis filter bank 802,

is the sub-filtered signal for the number k _s + m of the analysis filter bank 802,

is the numbered SL + s _subband signal of the three-stage analysis filter 800, and the rest of the symbols are the same as described above. B _{M , m} and k _s are calculated according to formulas (4) and (6) respectively (where s ranges between [1, S _M ]).

In the high analysis filter bank 803, in order to match the operation of the subband response precompensator 810 in formula (19), the b _k settings of the IIR subfilters 811 are changed to:

其中f _HIIR,k 、BW _HIIR,k 分別為該高分析濾波器組803之編號k IIR子濾波器之中心頻率與頻寬，其餘符號皆同前述。該等IIR子濾波器811依公式(1)(2)(24)運算(式中

以

代入)。該高分析濾波器組803的編號s子帶信號即該三段式分析濾波器組800的編號S _L +S _M +s子帶信號，其可表示為：

Wherein f _{HIIR , k} , BW _{HIIR , k} are respectively the center frequency and bandwidth of the sub-filter k IIR of the high analysis filter bank 803 , and other symbols are the same as above. The IIR sub-filters 811 operate according to formulas (1) (2) (24) (where

by

substitute). The number s subband signal of the high analysis filter bank 803 is the number SL _{+ SM +} s subband signal of the three-stage analysis filter bank 800, which can be expressed as:

φ _{H , s} =- π + θ ‧( S _L + S _M + s ) (25)

其中φ _H,s 為該高分析濾波器組803之編號s子帶信號的相位旋轉量，k _s 為該高分析濾波器組803之編號s組合器選用的多個子濾波信號之最低編號，

為該高分析濾波器組803之編號k _s +m子濾波信號，

為該三段式分析濾波器800之編號S _L +S _M +s子帶信號，其餘符號同前描述。B _M,m 與k _s 分別依公式(4)(6)計算(式中s範圍介於[1,S _HFB ]間)。

where φ _{H , s} is the phase rotation amount of the sub-band signal number s of the high analysis filter bank 803, k _s is the lowest number of the multiple sub-filter signals selected by the combiner of the number s of the high analysis filter bank 803,

filter the signal for the number k _s + m sub of the high analysis filter bank 803,

is the numbered SL _{+ SM +} s subband signal of the three-stage analysis filter 800, and the rest of the symbols are the same as described above. B _{M , m} and k _s are calculated according to formulas (4) and (6) respectively (where the range of s is between [1, S _HFB ]).

Note that in the design of the two-stage analysis filter bank 700 and the three-stage analysis filter bank 800, the feedforward coefficients of the IIR sub-filters are not determined only by the bandwidth of the IIR sub-filters as in formula (3). Instead, it is changed to change with the bandwidth of the IIR sub-filter and the center frequency of the IIR sub-filter at the same time. Therefore, even if one of the analysis filter banks is changed to use equal-width subbands, the feedforward terms of the IIR subfilters cannot be calculated in the same way as the previous design. Simplify with a feedforward term.

In addition to being implemented by a physical device, the functions of the three-stage analysis filter bank 800 can also be implemented by a three-stage filter bank operation program executed in at least one processor. The three-stage filter bank operation program respectively executes the three filter bank operation procedures of the corresponding three sub-band groups on at least one sampling point of an input signal to obtain a plurality of sub-band signals. The definition of the three-subband group refers to the description of paragraph [0041]. Refer to the descriptions of paragraphs [0030]~[0033] for the operation procedure of the three-stage filter bank, and match the setting and calculation formulas of the three-stage analysis filter bank (refer to the descriptions of paragraphs [0042]~[0047]). Each of the subband signals includes at least one sample point.

Figure 9 is a design example of a two-stage analysis filter bank using a subband of unequal width (the solid line in the figure is the sub-band equivalent filter response, and the dotted line is the total response of the two-stage analysis filter bank), It adopts the two-stage analytical filter bank design described above, and uses a first-order binomial combination and rotator. The sampling frequency of the input signal to the analysis filter bank is set to 12kHz. The high-frequency side of the analysis filter bank is divided into 7 sub-bands between double frequencies, and the low-frequency side is equal-width sub-bands (3 equal-width sub-bands below 1 kHz), so the DC to Nyquist frequencies are divided into 17 sub-bands in total. It is worth noting that the overall impulse response distortion of this system is clearly visible, which is completely different from the nearly ideal overall impulse response of the aforementioned equal-width subband analysis filter bank. This is caused by the large difference in subband bandwidths, resulting in large differences in the group delays of each subband.

Figure 10 is also a design example of a two-stage analysis filter bank, which is similar to that of Figure 9 The high-frequency side of the example is also divided into 7 subbands between double frequencies, and there are 6 equal-width subbands below 1kHz. The frequency resolution on the low-frequency side is nearly doubled, but the total number of subbands (23) is only 6 more than the example in Figure 9. Therefore, according to the requirements of the application, the designer can effectively reduce the analysis filtering by using the configuration of the unequal width sub-bands on the premise of maintaining the frequency resolution of the low-frequency part of the spectrum or the spectrogram (that is, the plot of the spectrum versus time). The number of subbands required by the device group.

FIG. 11 is a design example of a three-stage analysis filter bank, which is configured in the same manner as the non-equal-width subbands in the example of FIG. 10 . The sub-band pre-compensator in the three-stage analysis filter bank of this example provides better stop-band attenuation for the sub-band equivalent filter from the corresponding intermediate frequency sub-band to the high-frequency sub-band, but only slightly increases the computational complexity and Total response group delay (approximately add one sample time, 0.083ms).

FIG. 12 is a structural diagram of a filter bank system according to a fifth embodiment of the present invention. The filter bank signal processing system 1200 includes an analysis filter bank 1201 , a decimator 1202 , a core digital signal processing unit 1203 , and a subband combiner 1204 . The analysis filter bank 1201 performs frequency division filtering processing on an input signal (Note) according to a plurality of corresponding sub-bands to generate a plurality of sub-band signals. The implementation of the analysis filter bank 1201 can adopt the aforementioned analysis filter bank (refer to the description of paragraphs [0016]~[0024]), the two-stage analysis filter bank (refer to paragraphs [0035]~[0038]) description), or the three-stage analysis filter bank (refer to the description of paragraphs [0041]~[0046]).

Note: In acoustic applications, the input signal is usually a digitized waveform, which may come from An analog-to-digital converter output is either from a signal storage device, or is input to the filter bank signal processing system 1200 after downsampling the sampling frequency to preserve only the audible frequency range of the listener. Downsampling avoids wasting computation on high-frequency sounds that are not perceived by the listener. In addition, it can also be avoided that the waveform of high-frequency sound that is not perceived by the listener occupies a limited dynamic range of numerical operations. In fundamental-band signal processing applications, the input signal may come from an analog-to-digital converter output, or be downsampled and input to preserve the in-band signal, exclude out-of-band signals, and optimize numerical operations Dynamic Range.

The decimator 1202 decimates the sub-band signals at a rate N , that is, the sub-band signals corresponding to the same time are arranged in frequency at every one decimation period ( N sub-band signal sampling times) to generate a plurality of input spectrums One of the input spectrum. Let y _{FB , s} be the number s subband signal of the analysis filter bank, then the input spectrum can be expressed as: Y _h ={ y _{FB ,1} [ hN ], y _{FB ,2} [ hN ],.. y _{FB , S} [ hN ]}, where h is the time scale of the input spectrum. If the core digital signal processing unit 1203 does not use phase information, it can only extract the amplitudes (absolute values) of the sub-band signals, that is, the amplitudes of the sub-band signals corresponding to the same time are arranged in frequency to generate a plurality of input spectrums An input spectrum, which can be expressed as: Y _h ={| y _{FB ,1} [ hN ]|,| y _{FB ,2} [ hN ]|,..| y _{FB , S} [ hN ]|}. Furthermore, in order to satisfy Nyquist's theorem and reduce the energy of the folded components in the spectrum after the decimation process, the frame rate f _SAM / N of the input spectrum after the decimation process must be higher than the widest subband bandwidth.

The core digital signal processing unit 1203 for each of the input spectrums The specified digital signal processing is performed to determine a plurality of subband weights corresponding to the subbands at each time. The specified digital signal processing may include various types of frequency domain signal processing, such as fundamental frequency signal processing or equalization of acoustic processing, or dynamic range compression and noise reduction of acoustic processing. , dereverberation, source separation, feedback reduction or howling reduction...etc. Each of the above signal processing functions can be equivalent to adjusting the intensity or phase of each frequency component of a spectrum with a weight to obtain an output spectrum. The combining function of the multiple signal processing is also equivalent to adjusting the intensity or phase of each frequency component of the input spectrum with a weight to obtain a corresponding modified spectrum. Therefore, the ratio of the modified spectral value near the center frequency of each subband to the input spectral value can be calculated to determine the subband weight of the corresponding subband one.

The subband combiner 1204 performs a weighted sum operation on the subband signals with the corresponding subband weights to generate an output signal, and the operation can be expressed as:

其中g _s 為編號s子帶信號相應之權重，y為該濾波器組式信號處理系統1200之該輸出信號，其餘符號同前述。該輸出信號近似於圖1被修改子帶信號補零後通過該合成濾波器組105所得輸出信號。該子帶組合器1204除相較實施該合成濾波器組105節省運算外，另一個優點是避免了該合成濾波器組105再加長輸出信號的延遲時間。

Where g _s is the corresponding weight of the sub-band signal numbered s , y is the output signal of the filter bank type signal processing system 1200, and other symbols are the same as the above. The output signal is similar to the output signal obtained by passing through the synthesis filter bank 105 after the modified subband signal of FIG. 1 is zero-filled. In addition to saving operations compared to implementing the synthesis filter bank 105, the subband combiner 1204 has another advantage in that it avoids the synthesis filter bank 105 from increasing the delay time of the output signal.

In acoustic applications, the input and output signals of the system are both real numbers. If the corresponding weights of the sub-bands provided by the core signal processing unit 1203 are also of the real number type (without phase information), the operation can be simplified as taking out the real parts of the sub-band signals respectively, and multiplying the signals provided by the core signal processing unit 1203 The corresponding weights are summed up:

其中real為取實部之函數，其餘符號同前述。若該核心信號處理單元1203提供之相應各子帶信號的權重為複數型態(含相位資訊)，則可分別將該等子帶信號乘上該核心信號處理單元1203提供的相應權重後，取其實部信號加總：

Among them, real is the function of taking the real part, and the rest of the symbols are the same as above. If the weights of the corresponding sub-band signals provided by the core signal processing unit 1203 are complex numbers (including phase information), then these sub-band signals can be multiplied by the corresponding weights provided by the core signal processing unit 1203 to obtain In fact, the external signals are summed up:

其符號皆同前述。

The symbols are the same as above.

In addition to being implemented by a physical device, the functions of the filter bank signal processing system 1200 can also be implemented by an equivalent program executing on at least one processor. FIG. 13 is a flowchart of a filter bank type signal processing procedure according to the sixth embodiment of the present invention. Because the processing delay needs to be shortened as much as possible in real-time signal processing applications, this process step processes a continuous input signal in repeated segments; an output signal segment obtained in the previous step is immediately used for the subsequent steps for operation, without waiting for the previous step to obtain a complete output. Signal. The following paragraphs [0052] to [0055] are also referred to when describing the flow steps of the filter bank type signal processing program. Word.

In FIG. 13, at least one sampling point of an input signal is prepared (step S200).

A filter bank operation procedure is performed on the at least one sampling point of the input signal to obtain a plurality of subband signals (step S201 ). The implementation of the filter bank operation program can use the aforementioned filter bank operation program (refer to the description of paragraphs [0030]~[0033]), the two-stage filter bank operation program (refer to the description of paragraph [0039]) ), or the three-stage filter bank operation program (refer to the description of paragraph [0048]). Each of the subband signals includes at least one sample point.

It is checked whether a decimation period has ended (step S202). If it ends, start to count a new extraction cycle, and continue to execute from step S203; otherwise, continue to execute from step S205.

The subband signals or their amplitudes are extracted to obtain an input spectrum (step S203). Referring to the description in paragraph [0053], this means arranging the subband signals or their amplitudes corresponding to the same time into the input spectrum.

Execute a core signal processing procedure on the input spectrum to determine a plurality of subband weights corresponding to the subbands (step S204). Referring to the description in paragraph [0054], the core signal processing program corresponds to the function of the core signal processing unit 1203 of the fifth embodiment, which obtains a modified spectrum by processing the input spectrum through a specified frequency domain signal. Therefore, the ratio of the modified spectral spectral value to the input spectral spectral value near the center frequency of each subband can be calculated, It determines the corresponding sub-band weight of the sub-band.

A weighted sum operation is performed on the sub-band signals corresponding to a plurality of sampling points at the same time or their real parts with the sub-band weights to obtain at least one sampling point of an output signal (step S205 ). Then, it returns to step S200. Referring to the description of paragraph [0055], the weighted sum operation adopts the operation of the corresponding formula (27). If the output signal is of real type, the weighted sum operation can be simplified to the operation of the corresponding formula (29). If the sub-band weights determined by the core signal processing program are in the form of real numbers, the weighted sum operation can use the operation of the corresponding formula (28).

Because the IIR filter with the lowest order is adopted, the filter is shared among subbands, and the phase rotation without complex multiplication is used, the computational requirement of the analysis filter bank proposed by the present invention is compared with that of other types of analysis filter banks. Low. Taking the filter bank system corresponding to a total of S subbands as an example, if the analysis filter bank adopts a first-order binomial combination and rotator, then each sampling point of the output signal only needs S + 1 complex multiplications in the Feedback term of the IIR subfilter operation, 1 to S +1 real multiplications in the feedforward term of the IIR subfilter operation, one real multiplication in the subband response precompensator, and S real multiplications in the Subband combiner (the above excludes the operation requirement of the core digital signal processing unit), that is to say, the filter bank system architecture only needs one complex multiplication and one to two real multiplications per subband. However, if the number of sub-bands set is large or the order of the binomial is increased, the calculation amount of the filter bank system architecture will still be significantly higher than that of the AMS system architecture implemented by fast Fourier transform/inverse transform, so there are still room for improvement.

FIG. 14 is a block diagram of a mixed signal processing system according to a seventh embodiment of the present invention. The hybrid signal processing system 1400 includes a framing and time-frequency converter 1401, analysis filter banks 1402, a decimator 1403, a core digital signal processing unit 1404, a plurality of subband combiners 1405, and a frequency - Time converter 1406. Compared with the filter bank type signal processing system 1200 of the fifth embodiment, the hybrid audio processing system 1400 is equipped with time-frequency conversion to further reduce computing requirements. The following describes the implementation method of each component of the hybrid audio processing system 1400 .

R/2)，並將其每一信號幀作一R點之時-頻轉換(例如短時傅利葉轉換，離散傅利葉轉換..等)以產生多個頻譜之一頻譜。該R點之時-頻轉換相當於將全頻段(DC至該輸入信號取樣頻率f _SAM )切分為R個等頻寬頻帶並作一倍率N之抽取。該等頻譜相應同一頻帶的多個頻譜取樣點則為R個帶信號之一帶信號，其取樣頻率降為f _SAM /N。若採用一R點之短時傅利葉轉換，其可表示為： The framing and time-frequency converter 1401 divides an input signal into multiple signal frames ( N

R /2), and perform a time-frequency conversion (such as short-time Fourier transform, discrete Fourier transform, etc.) for each signal frame at an R point to generate one spectrum of multiple spectrums. The time-frequency conversion at the R point is equivalent to dividing the full frequency band (DC to the input signal sampling frequency f _SAM ) into R equal-bandwidth frequency bands and decimation by a factor of N. The spectrum sampling points corresponding to the same frequency band are one of the R band signals, and the sampling frequency is reduced to f _SAM / N . If the short-time Fourier transform of an R point is used, it can be expressed as:

其中g為頻帶編號，h為幀編號，亦為該等帶信號之時間足標，x _BAND,g 為編號g帶信號，x為該輸入信號，W _ANA 為該R點之短時傅利葉轉換之分析窗函數，其參數在[0,R-1]範圍內有非零值，其餘符號同前述。短時傅利葉轉換及其逆轉換運算公式可參照參考文獻4、參考文獻5之說明。又若輸入為聲學波，則系統僅需處理包含DC及Nyquist頻率之單側頻譜中的帶信號，g範圍可限縮至[0,R/2]。

Where g is the frequency band number, h is the frame number, and is also the time scale of the band signals, x _{BAND , g} is the numbered g band signal, x is the input signal, W _ANA is the short-time Fourier transform of the R point Analysis window function, its parameters have non-zero values in the range of [0, R -1], and other symbols are the same as above. For the short-time Fourier transform and its inverse transform formula, please refer to the descriptions in Reference 4 and Reference 5. If the input is an acoustic wave, the system only needs to process the band signal in the one-sided spectrum including the DC and Nyquist frequencies, and the g range can be limited to [0, R /2].

The analysis filter banks 1402 respectively filter and frequency-divide the band signals numbered 0 to R-1 to generate a plurality of sub-band signals, wherein each analysis filter bank corresponds to a plurality of sub-bands sub-segmented in a frequency band where the band signal is located. The implementation of each of the analysis filter banks 1402 may employ the analysis filter bank described above (refer to the description of paragraphs [0016] to [0024]), the two-stage analysis filter bank (refer to paragraph [0035]) ]~[0038]), or the three-stage analysis filter bank (refer to the description of paragraphs [0041]~[0046]). If the input is a real number type (eg, acoustic wave), the analysis filter banks 1402 only need to filter and divide the signals in the numbered 0 to R/2 bands of the corresponding single-sided spectrum to generate a plurality of sub-band signals. The decimator 1403 decimates the subband signals or their amplitudes by a factor M to generate one input spectrum of a plurality of input spectrums. After decimation, the frame rate of the input spectra is reduced to f _SAM /( MN ), which must still be higher than the bandwidth of the widest subband of the subbands to satisfy Nyquist's theorem.

The core digital signal processing unit 1404 performs specified frequency domain signal processing on each of the input spectrums to determine subband weights of the subband signals corresponding to each of the band signals (this function is the same as the fifth Core digital signal processing of an embodiment unit 1203).

Each of the subband combiners 1405 performs a weighted sum operation on the subband signals corresponding to one of the band signals of the subband signals with their corresponding subband weights to generate one of a plurality of modified band signals Modify the band signal. This operation can be expressed as:

其中y _BAND,g 為編號g被修改帶信號。S _g 為相應頻帶編號g之子帶的數量，w _g,v 為相應頻帶編號g之編號v子帶信號的子帶權重，其餘符號同前述。若輸入為聲學波，則該等子帶組合器1405產生之該等被修改帶信號僅相應於單側頻譜範圍，即公式(31)的g範圍限縮至[0,R/2]。

Where y _{BAND , g} is the number g is modified with the signal. S _g is the number of sub-bands corresponding to the frequency band number g , w _{g , v} are the sub-band weights of the sub-band signals of the number v corresponding to the frequency band number g , and the rest of the symbols are the same as described above. If the input is an acoustic wave, the modified band signals generated by the sub-band combiners 1405 only correspond to a one-sided spectral range, that is, the g range of equation (31) is limited to [0, R /2].

Finally, the frequency-time converter 1406 extracts the R sample points of the modified band signal at each time to perform a frequency-time conversion at point R (which is an inverse conversion method of the short-time Fourier transform at point R ). ) to generate an output signal. If the output signal is in the form of a real number such as an acoustic wave, then the complex conjugates of the modified band signals are used as a plurality of modified band signals on the symmetrical side of the spectrum, which can be expressed as:

該R點之頻-時轉換可採用一R點之加權疊加法(weighted overlap-add method，其為公式(30)之該R點之短時傅利葉轉換之一種逆轉換方法)以重建該輸出信號，其表示為：

The frequency-time conversion of the R point can use a weighted overlap-add method of the R point (which is an inverse conversion method of the short-time Fourier transform of the R point in formula (30)) to reconstruct the output signal , which is expressed as:

其中y _h 為編號h被修改信號幀，y為該輸出信號，W _SYN 為該R點之加權疊加法之合成窗函數，其參數在[0,R-1]範圍內有非零值，其餘符號同前述。若輸出信號為音訊，則公式(33)之運算可只取實部，亦即：

Where y _h is the modified signal frame numbered h , y is the output signal, W _SYN is the synthesis window function of the weighted superposition method of the R point, and its parameters have non-zero values in the range of [0, R -1], and the rest Symbols are the same as above. If the output signal is audio, the operation of formula (33) can only take the real part, that is:

其符號皆同前述。

The symbols are the same as above.

In this embodiment of the system, the sampling frequency of each analysis filter bank is reduced by time-frequency conversion, so that under the condition that the total number of subbands is the same, the computation amount of each subband can be greatly reduced. However, the signal processing delay of this system is the analysis filter bank delay plus the delay of the time-frequency conversion/inverse conversion (which is about the length of one frame). The cost of increasing the frame length and frame spacing of time-frequency conversion is still increasing the delay, so the choice of the frame length still depends on the designer's trade-off between the amount of computation and the delay of signal processing at the system level (selecting an appropriate frame length will increase the amount of system computation. down to AMS system architectures implemented with short-time Fourier transform/inverse transform, but with improved signal processing latency to an acceptable level).

The known application limitations and suggested processing methods of the system architecture based on the analysis filter bank proposed by the present invention are as follows:

- The frequency responses of the sub-band equivalent filters of the analysis filter bank are highly overlapping each other. Considering the situation that the number of sub-filtered signals shared by adjacent two combiners is a fixed number ( P ), if the lower-order binomial combination and rotator are used to design the analysis filter bank, the overlap of its frequency responses will be higher. When considering the design of the fixed-order term combiner, the larger the P value, the higher the overlap of the frequency response. When the overlap of the frequency responses is high, a response error may occur when the system implements a graphic equalizer (ie, an equalizer that can arbitrarily specify multiple frequency-corresponding gain values). Taking the first-order binomial combination and rotator to design the analysis filter bank as an example, if a single subband signal is removed during subband combination, the spectral attenuation of the corresponding frequency will be lower than 10dB. Therefore, if the signal processing algorithm in the system wants to perform a notching operation, that is, it wants to provide a high amount of attenuation near a specific frequency point, it is necessary to reduce the gain of multiple adjacent subbands at the same time to have sufficient effect.

- Limitation of frequency selectivity of the equivalent filters of each subband in the analysis filter bank (transition bands where the frequency range is not narrow and stopbands with limited attenuation). In addition, the response of the equivalent filter of each subband generally has a nonlinear phase, and the system may produce response errors when implementing functions such as graphic equalizers. Considering that the signal gain of the signal processing algorithm for some subbands is much larger than that of the adjacent subbands (for example, more than 20dB), the overall response of the analysis filter bank may be different from the expected gain in the adjacent subbands of these high gain subbands. different. Therefore, if there is a need to greatly increase the gain, it is recommended that the subband weight should be adjusted asymptotically when the signal processing algorithm such as wide dynamic range compression increases the subband weight. Heavy, that is, reduce the weight difference between adjacent sub-bands, and increase the number of sub-bands of the analysis filter group as needed. For example, when compensating for severe high-frequency hearing loss, the number of high-frequency sub-bands can be increased to reduce the number of adjacent sub-bands. weight gap.

-Due to the lack of a synthesis filter bank in the aforementioned filter bank system architecture, there is no anti-aliasing function provided by the synthesis filter bank as shown in FIG. , it is necessary to slow down the speed of weight change over time.

In addition to being implemented by a physical device, the functions of the mixed-signal processing system 1400 can also be implemented by an equivalent program executing on at least one processor. FIG. 15 is a flowchart of a mixed signal processing procedure according to an eighth embodiment of the present invention. When describing the flow steps of the mixed-signal processing program below, reference is made to the description texts in paragraphs [0065] to [0069].

In FIG. 15, at least one audio frame of an input audio is prepared (step S300).

A time-frequency conversion operation is performed on the at least one audio frame of the input audio to obtain a plurality of band signals (step S301 ). The time-frequency conversion operation adopts the operation of the corresponding formula (30), which can refer to the description of paragraph [0065]. Each of the band signals includes at least one spectral sample point corresponding to the same frequency band.

A filter bank operation procedure is respectively performed on the equal-band signals to obtain a plurality of sub-band signals (step S302). Referring to the description of paragraph [0066], the filter bank operation program A plurality of sub-bands sub-segmented in a frequency band corresponding to a band of signals. The implementation of the filter bank operation program can use the aforementioned filter bank operation program (refer to the description of paragraphs [0030]~[0033]), the two-stage filter bank operation program (refer to the description of paragraph [0039]) ), or the three-stage filter bank operation program (refer to the description of paragraph [0048]). Each of the subband signals includes at least one sample point.

It is checked to see if a decimation period has ended (step S303). If it ends, start to count a new extraction cycle, and continue to execute from step S304; otherwise, continue to execute from step S306.

The subband signals or their amplitudes are extracted to obtain an input spectrum (step S304). As in step S203 of the sixth embodiment, this step is to arrange the subband signals or their amplitudes corresponding to the same time according to frequency into the input spectrum.

A core signal processing procedure is performed on the input spectrum to determine a plurality of subband weights of a plurality of subband signals corresponding to each of the band signals (step S305). The function of this program is the same as that of the core signal processing program of the sixth embodiment.

Performing a weighted sum operation on the subband signals corresponding to each of the band signals and the corresponding subband weights to obtain one modified band signal of a plurality of modified band signals (step S306 ), which includes at least one sampling point. The weighted sum operation adopts the operation of the corresponding formula (31).

A multiple sampling point corresponding to the same time of the modified band signals is subjected to a A frequency-time conversion operation is performed to obtain a plurality of sampling points of an output signal (step S307). Then, it returns to step S300. The frequency-time conversion operation adopts the operation of the corresponding formulas (32) to (35), and refer to the description of paragraph [0069].

While the present invention has been described above with reference to preferred embodiments and illustrative drawings, it should not be construed as limiting. Those skilled in the art can make various modifications, omissions and changes to the form and the content of the specific examples, all without departing from the claimed scope of the claims of the present invention.

101: Analysis Filter Banks

201: Subband response precompensator

202: Multiple first-order infinite impulse response (IIR) subfilters

203: Multiple Binomial Combinations with Spinners

Claims (22)

An analysis filter bank corresponding to a plurality of sub-bands, which filters and frequency-divides an input signal according to the sub-bands to generate a plurality of sub-band signals, the sub-bands are of equal width, and the analysis filter bank comprises: a sub-band A response pre-compensator, which performs a linear filtering process on the input signal to generate a response pre-compensation signal; a plurality of sub-filters with different center frequencies, which respectively process the response pre-compensation signal into a complex first-order infinite impulse responsive to the filtering process to generate a plurality of sub-filtered signals; and a plurality of binomial combinations and rotators based on a set of binomial weights, each of which performs a weighted sum operation on at least two sub-filtered signals with the set of binomial weights , and rotate the result of the weighted sum operation by a phase with the center frequency of the corresponding sub-band to generate a sub-band signal of the sub-band signals, wherein the at least two sub-filtered signals are adjacent by at least two center frequencies of the sub-filters The child filter is generated. The analysis filter bank of claim 1, wherein two combinations of corresponding two frequency adjacent subbands share at least one subfiltered signal of the subfiltered signals with the rotator. The analysis filter bank of claim 2, wherein the phase difference between two combinations of adjacent subbands corresponding to two frequencies and two rotations of the rotator is an integer multiple of -π/2 arcs. The analysis filter bank of claim 3, wherein the linear filtering operation of the subband response precompensator is one of the input signal and a delayed version of the input signal Weighted sum operation. A two-stage analysis filter bank comprising two analysis filter banks as claimed in item 1, the two analysis filter banks being a low analysis filter bank corresponding to a low subband group and a corresponding high subband group The high analysis filter bank, the two analysis filter banks respectively filter and divide an input signal to generate a plurality of subband signals, and the linear filtering processing of the subband response precompensator of the low analysis filter bank is as follows A low-pass filtering process, the linear filtering operation of the sub-band response precompensator of the high analysis filter bank is a high-pass filtering operation. The two-stage analysis filterbank of claim 5, wherein the combinations and rotators of each of the two analysis filterbanks are based on the same set of binomial weights and correspond to two combinations of any two adjacent subbands A sub-filtered signal that shares the same number with the rotator. The two-stage analysis filter bank of claim 6, wherein the phase difference between the two frequency responses of the two subband response precompensator of the two analysis filter bank is a fixed value that is an integer multiple of π/2. The two-stage analysis filter bank of claim 7, wherein the sub-filter of the highest center frequency in the low analysis filter bank and the sub-filter of the lowest center frequency in the high analysis filter bank have the same center frequency and bandwidth. A three-stage analysis filter bank comprising three analysis filter banks as claimed in claim 1, the three analysis filter bank being a low analysis filter corresponding to a low subband group group, an analysis filter group corresponding to a middle subband group, and a high analysis filter group corresponding to a high subband group, the three analysis filter groups respectively filter an input signal to generate multiple subband signals, the linear filtering operation of the subband response precompensator of the low analysis filter bank is a low pass filtering operation, and the linear filtering operation of the subband response precompensator of the middle analysis filter bank is A bandpass filtering operation, and the linear filtering operation of the subband response precompensator of the high analysis filter bank is a highpass filtering operation. The three-segment analysis filter bank of claim 9, wherein the combinations and rotators of each of the three analysis filter banks are based on the same set of binomial weights and correspond to two combinations of any two adjacent subbands A sub-filtered signal that shares the same number with the rotator. The three-stage analysis filter bank of claim 10, wherein the phase difference of the three frequency responses of the three subband response precompensator of the three analysis filter bank is a fixed value of an integer multiple of π/2 in response to each frequency. The three-stage analysis filter bank of claim 11, wherein the sub-filter of the highest center frequency in the low analysis filter bank and the sub-filter of the lowest center frequency in the middle analysis filter bank have the same center frequency and bandwidth, And the sub-filter of the highest center frequency in the middle analysis filter bank and the sub-filter of the lowest center frequency in the high analysis filter bank have the same center frequency and bandwidth. A filter bank comprising an analysis filter bank as claimed in claim 1 The analysis filter bank performs frequency division filtering processing on an input signal to generate a plurality of sub-band signals, and the signal processing system also includes: a decimator, which extracts the sub-band signals or their amplitudes at a decimation rate to generating an input spectrum; a core digital signal processing unit, which performs specified digital signal processing on the input spectrum to determine a plurality of subband weights corresponding to the subband signals at each time; and a subband combiner, which The equal sub-band signals or their real parts are subjected to a weighted sum operation with the corresponding sub-band weights to generate an output signal. A hybrid signal processing system comprising a plurality of analysis filter banks as claimed in claim 1, the analysis filter banks respectively filter and frequency-divide a plurality of band signals to generate a plurality of subband signals, the hybrid signal processing system further Including: a framing and time-frequency converter, which divides an input signal into multiple signal frames of equal length and equal spacing according to time, and performs time-frequency conversion on the signal frames respectively to generate the band signals ; a decimator that extracts the subband signals or their amplitudes by a factor to generate an input spectrum; a core digital signal processing unit that performs specified signal processing on the input spectrum to determine each of the subband signals is the multiple subband weights of the corresponding multiple subband signals; a plurality of sub-band combiners, each of which performs a weighted sum operation on the corresponding sub-band signals of the one of the band signals with their corresponding sub-band weights to generate one of a plurality of modified band signals modified band signals; and a frequency-to-time converter that performs a frequency-to-time conversion on the modified band signals corresponding to a plurality of sampling points at the same time to generate an output signal. A filter bank operation program corresponding to a plurality of subbands, comprising the following steps: performing a linear filtering operation on at least one sampling point of an input signal to obtain at least one sampling point of a response precompensation signal; The at least one sampling point is subjected to a plurality of complex first-order infinite impulse response filtering operations with different center frequencies to obtain a plurality of sub-filtered signals, each sub-filtered signal includes at least one sampling point; and from the sub-filtered signals Select a plurality of subsets corresponding to the subbands, each of which contains the same number of at least two subfiltered signals obtained by at least two filtering operations adjacent to the center frequency, and each of the subsets corresponds to At least two sub-filtered signal sampling points at the same time perform a weighted sum operation with a set of binomial weights, and rotate the result of the weighted sum operation by a phase with the center frequency of the corresponding sub-band to obtain a sub-band signal of a plurality of sub-band signals , which includes at least one sampling point. The filter bank operation program of claim 15, wherein the corresponding two frequencies The two sub-filtered signal subsets of adjacent sub-bands have at least one identical sub-filtered signal. The filter bank operation program of claim 16, wherein the difference of the two rotation phases of the adjacent subbands of the corresponding two frequencies is an integer multiple of -π/2 arc. The filter bank operation procedure of claim 17, wherein the subbands are set to be of equal bandwidth, and the linear filtering operation is a weighted sum operation of the input signal and a delayed version of the input signal. A filter bank signal processing program comprising a step of executing a filter bank operation procedure as claimed in claim 15, the step of performing the filter bank operation procedure on at least one sampling point of an input signal to obtain a plurality of subband signals , each of which includes at least one sampling point, the filter bank signal processing program further includes the following steps: if a decimation period ends, extracting the subband signals or their amplitudes to obtain an input spectrum, the input spectrum Execute a core signal processing program to determine a plurality of sub-band weights corresponding to the sub-band signals, and start to calculate a new decimation cycle; and a plurality of sampling points or their real parts corresponding to the sub-band signals at the same time are given by A weighted sum operation is performed on the subband weights to obtain at least one sample point of an output signal. A hybrid signal processing program comprising a step of executing a filter bank operation procedure as claimed in claim 15, the step of respectively performing a filter bank operation procedure on a plurality of band signals to obtain a plurality of sub-band signals, each of which includes at least one sampling point, The mixed signal processing program further includes the following steps: performing a time-frequency conversion operation on at least one signal frame of an input signal to obtain the band signals, each of which includes at least one spectral sampling point corresponding to the same frequency band; if Once the decimation period ends, the subband signals or their amplitudes are extracted to obtain an input spectrum, and a core signal processing procedure is performed on the input spectrum to determine a plurality of sub-band signals corresponding to each of the plurality of sub-band signals weighted, and start to calculate a new decimation cycle; the sub-band signals corresponding to each of the band signals are subjected to a weighted sum operation with their corresponding sub-band weights to obtain a plurality of modified band signals. A modified band signal includes at least one sampling point; and a frequency-time conversion operation is performed on a plurality of sampling points corresponding to the same time of the modified band signal to obtain a plurality of sampling points of an output signal. A signal processing system comprising at least one processor, wherein the at least one processor performs a filter bank operation procedure such as any one of claims 15 to 18 or a filter such as claim 19 on at least one sample point of an input signal a processor-type signal processing procedure to obtain at least one sampling point of an output signal, or the at least one processor executes a mixed-signal processing procedure as in claim 20 for at least one signal frame of the input signal to obtain a sample point of the output signal multiple sampling points. An analysis filter bank corresponding to a plurality of subbands, which converts an input signal Perform filtering and frequency division according to the sub-bands to generate a plurality of sub-band signals, the sub-bands are of unequal width, and the analysis filter bank includes: a sub-band response pre-compensator, which performs a linear filtering operation on the input signal In order to generate a response pre-compensation signal, the response pre-compensator is set to make the response pre-compensation signal equal to the input signal under the unequal width sub-band configuration; a plurality of sub-filters with different center frequencies, respectively, the response The pre-compensated signal is subjected to a complex first-order infinite impulse response filtering process to generate a plurality of sub-filtered signals; and a plurality of binomial combinations and rotators based on a set of binomial weights, each of which converts at least two sub-filtered signals Perform a weighted sum operation with the set of binomial weights, and rotate the result of the weighted sum operation by a phase with the center frequency of the corresponding subband to generate a subband signal of the subband signals, wherein the at least two subfiltered signals are composed of At least two sub-filters with adjacent center frequencies of the sub-filters are generated.

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