CN107294512B - A non-uniform filter bank filtering method based on tree structure - Google Patents

Abstract

The invention provides a tree structure-based non-uniform filter bank construction method. The method comprises the following steps: a two-channel FIR orthogonal mirror image filter bank is used as a basic module, and a tree structure is adopted to build a non-uniform filter bank. Through the derivation of the reconstruction condition of the whole tree structure non-uniform filter bank, the complete reconstruction condition of the whole system is finally summarized as the design of a prototype filter meeting specific conditions. The designed prototype filter meets the reconstruction condition by adopting the iteration passband cut-off frequency, and in the specific design process of the prototype filter, the invention adopts the discrete weighted square error criterion, and compared with other methods, the criterion can realize better passband flatness characteristic and larger stopband attenuation. The design scheme of the invention effectively reduces the iteration complexity, can obtain larger stop band attenuation and better system reconstruction performance, and has important application value for radar broadband channelized receivers, voice and image signal processing.

Description

A non-uniform filter bank filtering method based on tree structure

technical field

The invention belongs to the technical field of filter banks, in particular to a non-uniform filter bank filtering method based on a tree structure.

Background technique

Multi-channel filter bank theory is widely used in radar, speech, image and other signal processing fields. The use of this technology effectively reduces data processing rate requirements, data storage space, and computational complexity. A filter bank system can divide the frequency band of the input signal through multiple filters with different frequency band characteristics in the front-end analysis module of the system, and then decelerate the input signal, and then process the sub-band signals of different frequency bands according to actual needs. Then in the back end of the system, the sub-band signal is reconstructed as much as possible into the required original signal through interpolation and the corresponding comprehensive filter bank, so the reconstruction performance of the whole filter bank is the focus of research in filter bank theory.

Filter bank is an important content in multi-rate signal processing, which has received extensive attention in recent years. Filter banks are widely used in communications, speech coding, audio coding and image signal processing. If the difference between the output and input of the system is only proportional in magnitude and there is a certain delay, the system is called a fully reconfigured system. The signal is decomposed into sub-bands for post-processing, which is convenient to use the frequency characteristics of the signal to obtain better results. In a system composed of an analysis filter bank and a synthesis filter bank, making the reconstructed signal at the output the same as the original signal at the input is usually the goal of filter bank design. However, from a practical point of view, under the condition that the distortion is controlled within a certain range, a design method with few restrictions, high efficiency and simplicity is more valuable. Multi-rate signal processing has a wide range of applications in communication, image coding, speech coding, radar and many other fields. Multi-rate technology can effectively reduce signal processing complexity, data transmission rate and storage capacity.

The non-uniform filter bank can divide the input signal into sub-signals with different frequency bandwidths according to actual needs, and has better flexibility. Compared with the uniform filter bank, the non-uniform filter bank is more flexible in dividing the frequency spectrum, so in recent years, the design research of the non-uniform filter bank has attracted the attention of many scholars. Many contributions have been made in design. But so far, achieving complete reconstruction of non-uniform filter banks remains a design challenge. Due to the large number of optimized parameters, it is difficult to design a completely reconstructed non-uniform filter bank. The design method of complete reconstruction is cumbersome, complex and difficult to implement. Therefore, in the actual design of non-uniform filter banks, the Flexible and simple approximate refactoring design. In the document "A simple design method for near perfect reconstruction nonuniform filter banks" published by Nguyen et al. in "Signal Processing IEEE Transactionson", a method of combining uniform filter banks is proposed to design non-uniform filter banks. Xie X's paper "A simple design method of linear-phase nonuniform filter banks with integer decimation factors" published in "Circuits and Systems" directly deduces the reconstruction relationship of non-uniform filter banks from the frequency domain, and uses this to design non-uniform filter banks. filter bank. Soni used a tree structure to design a non-uniform filter bank in the document "An Optimized Design of Non-uniform Filterbank using Blackman Window Family" (International Journal of Signal & Image Processing), and Kumar also used a tree structure in the document "Design of nearly perfect reconstructed non-uniform filter bank by constrained" In equiripple FIR technique" (Applied Soft Computing), a tree structure is also used to design a non-uniform filter bank, and the iterative objective function is simplified. The above non-uniform filter bank construction schemes have problems such as aliasing error, amplitude distortion, or phase distortion, and the reconstruction performance of the entire system needs to be improved.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a non-uniform filter bank filtering method based on tree structure, which solves the problem that the existing non-uniform filter bank construction scheme cannot design a non-uniform filtering system with good reconstruction performance.

The object of the present invention is achieved in this way:

A method for constructing a non-uniform filter bank based on a tree structure, comprising the following steps:

The first step: set the specific parameters of the prototype filter, including the coefficient length N, the pass-band cut-off frequency w _p , the stop-band cut-off frequency _ws , the initial iteration step size step, and the iteration termination error Recei;

The second step: design the prototype filter h _l (n) using the discrete weighted square error criterion, and then solve the value Real of the frequency response of h _l (n) at the orthogonal mirror point w=0.5π;

Step 3: Determine whether the actual error is less than the set termination error Recei, that is, whether the following formula holds:

|Real-0.7071|＜Recei (1)

If the above formula is true, use the filter h _l (n) to solve h _h (n), and then build a tree-structure non-uniform filter bank with a two-channel standard orthogonal mirror filter bank; if not, then further judge The size between Real and 0.707: if Real>0.707, then w _p =w _p -step, step=step/2; if Real<0.707, then w _p =w _p +step, step=step/2, each time After iteration, the step size step becomes half of the original; where h _h (n) represents a high-pass filter, and h _l (n) represents a low-pass filter.

The fourth step: update the pass-band cutoff frequency w _p , and then use the new w _p to design the low-pass filter h _l (n) again, and iterate successively until the error value is less than the given error range.

For a non-uniform filter bank filtering method based on tree structure, the prototype filter H _l (z) satisfies the deduced reconstruction conditions by iterating the passband cutoff frequency of the filter; in the specific design process of the prototype filter , a prototype low-pass filter is designed using the discrete weighted squared error criterion method.

where H _l (z) is the transfer function of the low-pass filter h _l (n).

For a non-uniform filter bank filtering method based on a tree structure, the discrete weighted square error criterion method includes the following specific processes:

Defining the Error Function Using Weighted Discrete Squared Error Criterion

E(w)=W(w)[A(w)-A _d (w)] (2)

where E(w) represents the weighted error between Ad (w) and A(w); _Ad (w) represents the magnitude function of h _d (n) to be approximated, and h _{d (} n) represents the ideal filter ; A(w) represents the amplitude function of h(n), h(n) represents the actual designed filter; W(w)≥0 is the weighting function.

The weighted discrete squared error Δ is defined as:

where (w _m , m=1, 2, . . . , L) are L sampling points in the frequency domain.

The magnitude function of the FIR filter is expressed as:

A(w)=Q(w)G(w) (4)

in:

Among them, Q(w)=cos(w/2), K=(N-1)/2, and N is the designed filter order.

The intermediate coefficient g(n) (n=1,2,...,K) is solved by the idea of optimization, and then the first half of the actual coefficient h(n) is solved according to the following formula, and then the actual coefficient h(n) is solved by symmetry. All coefficients h(n) of the required FIR filter.

Among them, n=1,2,...,K-1.

Substituting formulas (4) and (5) into formula (3), we get:

Now express the error function Δ in matrix form, and define the error vector Λ:

Λ=(Λ ₁ ,Λ ₂ ,...,Λ _L ) ^T (8)

in:

Then the total error function Δ can be expressed as:

Δ=Λ ^T Λ (10)

In matrix form, the error vector Λ can be expressed as:

Λ=W(QCg-A _d ) (11)

where W and Q are L×L matrices, namely:

C is an L×(K+1) matrix, that is:

A _d is a vector of L elements, that is:

Ad = [A _d (w ₁ ), _Ad (w ₁ ),..., _{Ad (} w _L )] (15)

When L=K+1, since WQC is an L×L matrix, it can be known from formula (11) that the solution with the error Δ equal to zero can be obtained by solving the equation WQCg=WA _d . Since the error Δ is equal to zero, the weighting matrix W at this time has no effect on the actually designed filter. When L>K+1, the number of equations is greater than the number of unknowns, so there is no solution to the equations. If the WQC matrix is a full-rank matrix at this time, then the error function Δ shown in formula (11) There is a unique minimal solution. At this point, the following equation can be solved, namely:

(WQC) ^T WQCg = (WQC) ^T WA _d WQC (16)

The intermediate coefficient vector g is solved, and then the unit impulse response h(n) of the actual design is solved by formula (6).

Described dual-channel FIR standard orthogonal mirror filter bank is based on the non-uniform filter bank filtering method of tree structure, and the specific design steps are:

Step 1: Design a dual-channel FIR standard quadrature mirror filter bank;

Step 2: Use the dual-channel FIR standard quadrature mirror filter bank as the basic module, and combine the tree structure to build a non-uniform filter bank;

Step 3: Derive the non-uniform filter bank reconstruction conditions designed by the method;

Step 4: Simplify the reconstruction conditions of the entire non-uniform filter bank as follows: the amplitude of the frequency response of the prototype FIR filter at the orthogonal point w=π/2 satisfies H _l (e ^jπ/2 )=0.7071;

Step 5: adopt the passband cutoff frequency of the iterative prototype filter to make it satisfy the reconstruction condition in step 4;

Step 6: In the specific design process of the prototype filter, the discrete weighted square error criterion method is used to design the prototype low-pass filter.

For a non-uniform filter bank filtering method based on a tree structure, the two-channel FIR standard orthogonal mirror filter bank builds a non-uniform filter bank with a tree structure including an analysis module and a synthesis module.

In the analysis module, the relationship conditions of the low channel filter H _l (z) and the high channel filter H _h (z) are set as:

H _h (z) = H _l (-z) (17)

Among them, H _l (z), H _h (z) are the transfer functions of the first channel and the second channel in the analysis module, respectively.

The filter relationship in the synthesis module and the analysis module is set as:

F _l (z)=H _h (-z), F _h (z)=-H _l (-z) (18)

Among them, F _l (z), F _h (z) are the transfer functions of the first channel and the second channel in the synthesis module, respectively.

For a non-uniform filter bank filtering method based on a tree structure, the reconstruction conditions of the tree structure non-uniform filter bank built by using the two-channel FIR standard orthogonal mirror filter bank are:

Among them, H _k (e ^jw ) represents the filter frequency response of the kth channel, w is the frequency point, π is the pi, and M represents the number of channels of the non-uniform filter bank.

The beneficial effects of the present invention are: compared with the existing design scheme, the present invention simplifies the iterative reconstruction conditions, and applies the discrete weighted square error criterion to the design of the non-uniform filter bank constructed by the tree structure, so that the entire While ensuring the linear phase of each channel, the filter system has further improved the stopband attenuation of each channel and the amplitude distortion of the entire system, thereby improving the reconstruction performance of the non-uniform filter bank.

Description of drawings

Fig. 1 is a tree structure 4-channel non-uniform filter bank of the present invention;

Fig. 2 is the equivalent diagram of 4 channels of tree structure of the present invention;

Fig. 3 is the performance comparison diagram of the FIR filter designed using different methods such as window function method, characteristic filtering method, equal ripple method, discrete weighted square error criterion in the present invention;

Fig. 4 is the non-uniform filter bank iteration algorithm flow chart of the present invention;

Fig. 5 is the prototype FIR filter amplitude response curve of the present invention;

Fig. 6 is a tree structure 6-channel non-uniform filter bank simulation diagram of the present invention;

FIG. 7 is an amplitude distortion diagram of a tree-structured 6-channel non-uniform filter bank of the present invention.

Detailed ways

Below in conjunction with the accompanying drawings, the design scheme in the present invention is specifically introduced:

Step 1: Adopt dual-channel FIR standard orthogonal mirror filter bank to build a non-uniform filter bank of tree structure, Fig. 1 is a tree structure 4-channel non-uniform filter bank of the present invention, Fig. 2 is a tree structure 4 of the present invention Channel equivalent diagram, in the dual-channel filtering system, the relationship conditions of the low-channel filter H _l (z) and the high-channel filter H _h (z) in the analysis module are set as:

H _h (z)=H _l (-z) (1)

The filter relationship in the synthesis module and the analysis module is set as:

F _l (z)=H _h (-z), F _h (z)=-H _l (-z) (2)

At this time, the whole system has no aliasing distortion and phase distortion.

Step 2: Each channel filter in Figure 2 can be expressed as:

and

Wherein, H ₀ (z), H ₁ (z), H ₂ (z), and H ₃ (z) are the transfer functions of each channel in FIG. 2 , respectively.

Step 3: At this time, the non-uniform filter bank reconstruction condition in Figure 2 is:

where H _k (e ^jw ) represents the filter frequency response of the kth channel.

Step 4: Substitute formulas (3) and (5) into the reconstruction condition (6) to simplify:

|H _l (e ^jw )| ⁶ +|H _l (e ^jw )| ⁴ |H _l (e ^j(π-w) )| ² +|H _l (e ^jw )| ² |H _l (e ^{j( π-w)} )| ² +|H _l (e ^j(π-w) )| ² =1(7)

In formula (7), take the orthogonal frequency point w=π/2 to simplify:

2|H _l (e ^jπ/2 )| ⁶ +|H _l (e ^jπ/2 )| ⁴ +|H _l (e ^jπ/2 )| ² =1 (8)

Solving higher-order equation (8), we get:

H _l (e ^jπ/2 )=0.7071 (9)

The number of channels of the non-uniform filter bank formed by the tree structure is extended to M, and the decimation and interpolation rate of each channel is set to (2 ^M-1 , 2 ^M-1 , 2 ^M-2 ,...,4,2), The coefficients of each channel in the equivalent non-uniform filter bank analysis module can be expressed as:

and

Substituting the coefficient relationship contained in formulas (10) and (11) into the M channel reconstruction conditional expression (6), we can get:

Substitute e ^jw for z in the above formula, and take the orthogonal frequency point w=π/2 to solve it, we get:

2|H _l (e ^jπ/2 )| ^2(M-1) +H _l (e ^jπ/2 )| ^2(M-2) +|H _l (e ^jπ/2 )| ^2(M-3) +…+|H _l (e ^jπ/2 )| ⁴ +|H _l (e ^jπ/2 )| ² =1 (13)

Solving higher-order equation (13) can get the same solution H _l (e ^jπ/2 )=0.7071 as equation (9). Therefore, the non-uniform filter bank constructed by using the dual-channel FIR standard quadrature mirror filter bank combined with the tree structure can be obtained. The reconstruction condition is H _l (e ^jπ/2 )=0.7071.

The passband cutoff frequency of the iterative prototype filter H _l (z) is adopted to satisfy the reconstruction condition (9). In the specific design process, the discrete weighted squared error criterion is used to design the prototype filter H _l (z). The method adopts the optimization idea to make the actually designed filter frequency response H(e ^jw ) infinitely close to the ideal frequency response H _d (e ^jw ), so as to minimize the error between the two. Compared with the window function method, the equiripple method and the characteristic filter method, the discrete weighted square error criterion can obtain a flatter passband and greater stopband attenuation under the same design parameters. The specific design process is as follows: Firstly, the weighted discrete square error criterion is used to define the error function.

E(w)=W(w)[A(w)-A _d (w)] (14)

The weighted discrete squared error Δ is defined as:

The number L of frequency sampling points is used to characterize the passband and stopband performance. The idea of designing an FIR filter in this method is to minimize the error Δ defined by formula (15). The magnitude function of the FIR filter is expressed as:

A(w)=Q(w)G(w) (16)

in:

Through the idea of optimization, the intermediate coefficient g(n) (n=1,2,...,K) is solved, and then the first half of the actual coefficient h(n) is solved according to the following formula, and then through symmetry, Solve for all the coefficients h(n) of the FIR filter actually required.

Among them, n=1,2,...,K-1.

Substituting formulas (16) and (17) into formula (15), we get:

Now express the error function Δ in matrix form, and define the error vector Λ:

Λ=(Λ ₁ ,Λ ₂ ,...,Λ _L ) ^T (20)

in:

Then the total error function Δ can be expressed as:

Δ=Λ ^T Λ (22)

In matrix form, the error vector Λ can be expressed as:

Λ=W(QCg-A _d ) (23)

where W and Q are L×L matrices, that is:

C is an L×(K+1) matrix, that is:

A _d is a vector of L elements, that is:

Ad = [A _d (w ₁ ), _Ad (w ₁ ),..., _{Ad (} w _L )] (27)

When L=K+1, because WQC is an L×L matrix, it can be known from formula (23) that the solution with the error Δ equal to zero can be obtained by solving the equation WQCg=WA _d . Since the error Δ is equal to zero, the weighting matrix W at this time has no effect on the actually designed filter. When L>K+1, the number of equations is greater than the number of unknowns, so the equations have no solution. If the WQC matrix is a full-rank matrix at this time, then the error function Δ shown in formula (23) There is a unique minimal solution. At this point, the following equation can be solved, namely:

(WQC) ^T WQCg = (WQC) ^T WA _d WQC (28)

The intermediate coefficient vector g is solved, and then the unit impulse response h(n) of the actual design is solved by formula (18).

In the following, the FIR filter is designed by the characteristic filter method, the equal ripple design method, the window function design method, and the discrete weighted square error criterion method, and the results are compared and analyzed. FIG. 3 is a performance comparison diagram of the window function method, the feature filtering method, the equal ripple method, and the discrete weighted square error criterion in the present invention, and the specific parameter performance is shown in Table 1.

Table 1 Comparison of specific parameters and characteristics of FIR filters constructed by different methods

It can be seen from Table 1 that under the same design parameters, the discrete weighted square error criterion can achieve greater stop-band attenuation, thereby better suppressing out-of-band signals.

Fig. 4 is the non-uniform filter bank iteration algorithm flow chart of the present invention, and the concrete design steps of non-uniform filter bank are provided below in conjunction with Fig. 4:

step 1:

The first step: set the specific parameters of the prototype filter, including the coefficient length N, the pass-band cut-off frequency w _p , the stop-band cut-off frequency _ws , the initial iteration step size step, and the iteration termination error Recei;

The second step: design the prototype filter h _l (n) using the discrete weighted square error criterion, and then solve the value Real of the frequency response of h _l (n) at the orthogonal mirror point w=0.5π;

Step 3: Determine whether the actual error is less than the set termination error Recei, that is, whether the following formula holds:

|Real-0.7071|＜Recei (29)

If the above formula holds, use the filter h _l (n) to solve h _h (n), and then build a tree-structured non-uniform filter bank with a two-channel FIR standard quadrature mirror filter bank; if not, then further Determine the size between Real and 0.707: if Real>0.707, then wp _{= wp} -step,step=step/2; if Real<0.707,wp _{= wp} +step,step=step/2, every time After iteration, the step size step becomes half of the original; where h _h (n) represents the high-pass filter.

The fourth step: update the pass-band cutoff frequency w _p , and then design the filter h _l (n) again with the new w _p , and iterate successively until the error value is less than the given error range.

In order to verify the effectiveness of the present invention, simulation experiments are carried out. The present invention is used to design a 6-channel non-uniform filter bank with decimation and interpolation rates of each channel respectively (16, 16, 8, 4, 4, 4), and the iteration termination error is set to Recei=10 ^-4 to ensure good accuracy , the iteration step size is set to step=0.15π. And define the amplitude distortion function Amdis to characterize the reconstruction performance of the whole system, namely:

where H _m (e ^jw ) represents the filter frequency response of the mth channel.

The specific parameters of the prototype filter h _l (n) are: coefficient length N=63, pass-band cut-off frequency w _p = _0.41π , stop-band cut-off frequency ws =0.65π. The filter h _l (n) is constructed by using the discrete weighted square error criterion. Fig. 5 is the amplitude response curve of the prototype FIR filter of the present invention. It can be seen from Fig. 5 that the stop-band attenuation is A _s =-133dB at this time. Fig. 6 is a simulation diagram of a tree-structured 6-channel non-uniform filter bank of the present invention, and Fig. 7 is an amplitude distortion diagram of a tree-structured 6-channel non-uniform filter bank of the present invention. At this time, the maximum value of the amplitude distortion is max(Amdis)= 1.3×10 ^-3 . The method of the present invention is compared with the existing design method, as shown in Table 2.

Table 2 Performance comparison of different design methods

Table 3 The performance comparison between the design method in this paper and the Kumar design method

It can be seen from Table 3 that compared with the Kumar design method, the design method in this paper improves the stopband attenuation by 59.6% on average and the amplitude distortion by 37.6% on average. Based on the above analysis, it can be seen that after the discrete weighted square error criterion is applied to the design of the non-uniform filter bank built by the tree structure, the entire filter system can ensure the linear phase of each channel, while the stopband attenuation of each channel and the whole system. Amplitude distortion is further improved, which in turn improves the reconstruction performance of non-uniform filter banks.

Claims (6)

1. A non-uniform filter bank filtering method based on a tree structure is characterized in that:

the first step is as follows: setting specific parameters of the prototype filter, including coefficient length N and passband cut-off frequency w_pStop band cut-off frequency w_sInitial iteration step and iteration termination error Recei;

the second step is that: prototype filter h design using discrete weighted square error criterion_l(n) then solve for h_l(n) a value Real of the frequency response at the quadrature mirror point w ═ 0.5 pi;

the third step: judging whether the actual error is smaller than a set termination error Recei, namely whether the following formula is satisfied:

|Real-0.7071|＜Recei (1)

if the above equation is true, the filter h is used_l(n) solving for h_h(n), then, building a tree-structure non-uniform filter bank by using a two-channel standard orthogonal mirror filter bank; if not, further judging the size between Real and 0.707: if Real > 0.707, w_p＝w_p-step, step ═ step/2; if Real is less than 0.707, w_p＝w_p+ step, step being step/2, step becoming half of the original after each iteration; wherein h is_h(n) denotes a high-pass filter, h_l(n) represents a low-pass filter;

the fourth step: updating the passband cutoff frequency w_pThen using the new w_pRedesigning the low-pass filter h_l(n) sequentially iterating until the error value is smaller than a given error range;

by iterating the filter passband cut-off frequency, the prototype filter H_l(z) satisfying the derived reconstruction condition; in the specific design process of the prototype filter, designing the prototype low-pass filter by adopting a discrete weighted square error criterion method;

wherein H_l(z) is a low-pass filter h_l(n) a transfer function;

the discrete weighted square error criterion method comprises the following specific processes:

(1) defining an error function using a weighted discrete square error criterion

E(w)＝W(w)[A(w)-A_d(w)](2)

Wherein E (w) represents A_d(w) weighted error between (w) and a (w); a. the_d(w) represents h to be approximated_d(n) amplitude function, h_d(n) represents an ideal filter; a (w) represents the amplitude function of h (n), and h (n) represents the actually designed filter; w (w) ≧ 0 is a weighting function;

(2) the weighted discrete squared error Δ is defined as:

wherein (w)_mM 1, 2.., L) is L sample points in the frequency domain;

(3) the amplitude function of the FIR filter is represented in the form:

A(w)＝Q(w)G(w) (4)

wherein:

wherein q (w) cos (w/2), K ═ N-1)/2, and N is the designed filter order;

(4) solving intermediate coefficients g (n) (1, 2,., K) through an optimization idea, solving the first half of actual coefficients h (n) according to the following formula, and then solving all coefficients h (n) of the actually needed FIR filter through symmetry;

wherein n is 1, 2., K-1;

(5) substituting the formulas (4) and (5) into the formula (3) to obtain:

now the error function Δ is represented in matrix form, defining an error vector Λ:

Λ＝(Λ₁,Λ₂,…,Λ_L)^T(8)

wherein:

the total error function Δ can be expressed as:

Δ＝Λ^TΛ (10)

in matrix form, the error vector Λ can be expressed as:

Λ＝W(QCg-A_d) (11)

where W and Q are L×L matrices, i.e.:

c is a matrix of L× (K +1), i.e.:

A_dis a vector of L elements, namely:

A_d＝[A_d(w₁),A_d(w₁),…,A_d(w_L)](15)

when L is K +1, because WQC is a L×L matrix, we can understand from equation (11) that WQCg is WA_dWhen L is more than K +1, the number of the equation set is more than the number of the unknown quantity, so that the equation set has no solution, if the WQC matrix is a column full rank matrix, a unique minimum solution exists in the error function delta shown in the formula (11), and the following equations can be solved:

(WQC)^TWQCg＝(WQC)^TWA_dWQC (16)

and solving an intermediate coefficient vector g, and further solving a unit impulse response h (n) of the actual design through a formula (6).

2. The tree-based non-uniform filter bank filtering method according to claim 1, wherein: the specific design steps are as follows:

step 1: designing a two-channel FIR standard orthogonal mirror filter bank;

step 2: a two-channel FIR standard orthogonal mirror filter bank is used as a basic module, and a non-uniform filter bank is built by combining a tree structure;

and step 3: deducing the reconstruction condition of the non-uniform filter bank designed by the method;

and 4, step 4: the reconstruction condition of the whole non-uniform filter bank is simplified as follows: the frequency response of the prototype FIR filter has an amplitude at the quadrature point w ═ pi/2 that satisfies H_l(e^jπ/2)＝0.7071；

And 5: passband cutoff frequency w using an iterative prototype filter_pMaking it meet the reconstruction condition in step 4;

step 6: in the specific design process of the prototype filter, the prototype low-pass filter is designed by adopting a discrete weighted square error criterion method.

3. The tree-based non-uniform filter bank filtering method according to claim 2, wherein: the non-uniform filter bank with the tree structure built by the two-channel FIR standard orthogonal mirror filter bank comprises an analysis module and a synthesis module.

4. A tree based non-uniform filter bank filtering method according to claim 3, characterized in that: low-channel filter H in non-uniform filter bank analysis module with tree-shaped structure built by two-channel FIR (finite impulse response) standard orthogonal mirror filter bank_l(z) and a high-pass filter H_h(z) the relational conditions are set as:

H_h(z)＝H_l(-z) (17)

wherein H_l(z)，H_h(z) are transfer functions of the first channel and the second channel, respectively, in the analysis module.

5. The tree-based non-uniform filter bank filtering method according to claim 2, wherein: the filter relationship between the synthesis module and the analysis module is set as:

F_l(z)＝H_h(-z),F_h(z)＝-H_l(-z) (18)

wherein, F_l(z)，F_h(z) are transfer functions of the first channel and the second channel, respectively, in the integrated module.

6. The tree-based non-uniform filter bank filtering method according to claim 2, wherein: the reconstruction condition of the tree-structure non-uniform filter bank built by adopting the two-channel FIR standard orthogonal mirror filter bank is as follows:

wherein H_k(e^jw) Represents the filter frequency response of the kth channel, w is the frequency point, pi is the circumferential ratio, and M represents the number of channels of the non-uniform filter bank.

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