A design method for low-complexity and high-precision variable fractional delay filter

Abstract

The present invention provides a design method for a low-complexity, high-precision variable fractional delay filter, comprising the following steps: step 1, using a Farrow architecture to implement a variable fractional delay filter VFD, and obtaining relevant parameters of the variable fractional delay filter VFD; step 2, pre-designing a sub-filter coefficient matrix, using a window function with adjustable parameters to design a sub-filter, and adjusting the frequency resolution of the variable fractional delay filter VFD under different orders; step 3, performing a least squares optimization solution, and performing polynomial fitting on the coefficient matrix obtained by the solution; and step 4, applying the coefficient matrix obtained by fitting to the Farrow architecture, thereby obtaining the coefficients of the variable fractional delay filter VFD based on the Farrow architecture. While ensuring the accuracy of group delay, the present invention avoids mathematical operations such as partial derivatives and double integrals, reduces the complexity of coefficient solution, and improves the calculation efficiency of the Farrow architecture variable fractional filter parameters.

Description

Technical Field

[0001] The invention belongs to the technical field of signal processing and communication, and in particular relates to a design method of a low-complexity, high-precision variable fractional delay filter. Background Art

[0002] In signal processing and communication systems, variable fractional delay (VFD) filters are widely used in sampling rate conversion, delay adjustment, and beamforming. Among the existing methods for implementing fractional delay, the Farrow architecture provides a flexible method for implementing variable fractional delay. The architecture consists of multiple sub-filters, whose filter coefficients and delay values ​​are independent of each other. Therefore, when the delay value changes, the filter coefficients do not need to be changed, saving a lot of computing and storage space. The key to the design of the Farrow architecture VFD filter lies in the solution of its coefficients. Existing sub-filter design methods include Lagrange interpolation, weighted least squares, minimax, and iterative algorithms based on mathematical optimization models. The Lagrange interpolation method is widely used because of its simple calculation, but when processing high-frequency signals, the filter performance drops sharply and the stability of the amplitude and frequency in the entire passband cannot be guaranteed. Weighted least squares and minimax methods are both designed to minimize errors. However, in the design process, matrix inversion and integral operations increase the complexity of the design, resulting in longer calculation time. In addition, the weight parameter adjustment process of the weighted least squares method is relatively complicated, which further aggravates the instability of the numerical calculation of the filter coefficients. Iterative algorithms based on mathematical optimization models can achieve higher accuracy, but such models are complex to establish, and the number of iterations and convergence cannot be guaranteed under different working conditions. Based on the above problems, in the design of communication systems, it becomes important to seek a method that is simple in calculation and can avoid complex matrix operations to design the VFD structure. Summary of the invention

[0003] Purpose of the invention: In view of the shortcomings of the prior art in designing fractional delay filters, the present invention proposes a method for designing VFD filters by using a windowing function. By adjusting parameters, the frequency resolution of variable fractional delay filters (VFDs) of different orders can be flexibly adjusted, thereby reducing the Gibbs phenomenon without increasing the order of the filter. Then, the least squares optimization solution is solved by using QR decomposition matrix to avoid ill-conditioned matrix inverse problems, so as to obtain VFD filter coefficients with lower computational complexity, and finally the filter performance is evaluated by evaluation criteria.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] The present invention discloses a design method of a low-complexity, high-precision variable fractional delay filter, comprising the following steps:

[0006] Step 1: Use Farrow architecture to implement variable fractional delay filter VFD, and obtain relevant parameters of variable fractional delay filter VFD, which include filter order K, window function width factor , time delay p, normalized angular frequency of the filter and polynomial order R;

[0007] Step 2, according to the relevant parameters of the variable fractional delay filter VFD, pre-design the sub-filter coefficient matrix, adopt the parameter-adjustable window function to design the sub-filter, and flexibly adjust the frequency resolution of the variable fractional delay filter VFD under different orders by adjusting the parameters, so as to reduce the Gibbs phenomenon without increasing the filter order;

[0008] Step 3, performing least square optimization solution according to the sub-filter coefficient matrix, only one matrix inversion is required in the process of solving the coefficients; using QR decomposition matrix to avoid ill-conditioned matrix inversion problem, so as to obtain the coefficients of the variable fractional delay filter VFD with lower computational complexity, and performing polynomial fitting on the coefficient matrix obtained by solving;

[0009] Step 4, applying the fitted coefficient matrix to the Farrow architecture, thereby obtaining the coefficients of the variable fractional delay filter VFD based on the Farrow architecture. The change of the delay amount does not require changing the filter coefficients, thereby improving the computational efficiency and storage space of the variable fractional delay filter VFD.

[0010] In step 1, the frequency response of the variable fractional delay filter VFD is derived from an actual filter impulse response, including:

[0011] A K-order finite impulse response It is expressed as:

[0012]

[0013] in is the coefficient of the k-th order filter, , , intermediate parameters represents the filter passband range; is the discrete Fourier transform factor, j is the imaginary unit;

[0014] Under different delay conditions, Expressed as a function with delay p as the independent variable , use an R-order polynomial to fit, the expression is:

[0015]

[0016] in represents the coefficient of the k-th order r-term sub-filter, r=0,1,…,R; ;

[0017] Will Substitute the expression In the Farrow architecture, we get the transfer function :

[0018]

[0019] The polynomial coefficient frequency response , the factor matrix of the discrete Fourier transform , T represents matrix transpose; delay matrix vector , represents the time delay p of the filter from the 1st order to the R+1th order fitting polynomial.

[0020] In step 1, the polynomial coefficient matrix It is expressed as:

[0021] ,

[0022] in Represents the coefficient matrix composed of R-term polynomial K-order sub-filters.

[0023] In step 2, the sub-filter coefficient matrix under different delay amounts is obtained by the following formula:

[0024] ,

[0025] in is the Gaussian window function; It is an ideal impulse response. Only when the delay value p is an integer multiple of the sampling point n, The expression is not 0. When the delay value p is a fractional multiple of the sampling point, the ideal filter impulse response is an infinite non-causal sinc function, expressed as:

[0026] ;

[0027] The calculation formula is:

[0028] ,

[0029] in is the window function width factor, which is also the standard deviation of the Gaussian random variable, and the intermediate parameter and Inversely proportional, the corresponding relationship is , is the length of the window function, . Gaussian window function The value of depends on the filter order K. When K is low, increasing , the main lobe becomes wider, the frequency resolution is not high, but the side lobe performance is increased, the spectrum leakage is reduced, so that the filter can obtain relatively flat amplitude-frequency and phase-frequency characteristics without increasing the order; when K is high, the , the main lobe becomes narrower, the frequency resolution increases, and different frequency components can be accurately distinguished.

[0030] In step 3, the least squares method is used, that is, the frequency response function of the actual filter is designed to approximate the frequency response function of the ideal filter and minimize the error function, which is achieved by the following formula:

[0031]

[0032] Among them, through the frequency band Multiply the error function by a non-negative weighting function , and integrate within the frequency band to obtain the optimized objective function ; Here, in order to reduce the computational complexity, we set ;

[0033] , , To calculate the filter coefficient correlation matrix; represents conjugation, is the frequency response of an ideal filter;

[0034] Filter coefficient matrix , is the coefficient of the K-th order filter;

[0035] Then the objective function Ask about The gradient of , through transposition transformation, we get the following expression:

[0036]

[0037] The matrix , is the cosine function matrix, expressed as: ,

[0038] Solving the filter coefficients involves matrices Find the inverse operation, but this matrix is ​​independent of the delay p, can be calculated in advance, and only needs to be calculated once;

[0039] matrix , is the real part operation, is the operation of taking the imaginary part, , are the real coefficient vector and imaginary coefficient vector of the actual filter coefficients respectively; , ;

[0040] The obtained filter coefficients are fitted with a polynomial:

[0041]

[0042] in represents the polynomial delay matrix; is the polynomial coefficient matrix corresponding to different time delays;

[0043] The different delays , represents the first polynomial delay, Represents the M+1th polynomial delay; each delay corresponds to a polynomial, forming a polynomial delay matrix ;

[0044] The matrix Decompose into an upper triangular matrix and an orthogonal matrix The product of , we get:

[0045]

[0046] Applying the coefficients obtained by the least squares fitting to the Farrow architecture yields:

[0047] .

[0048] In step 3, the polynomial delay matrix It is expressed as:

[0049] ,

[0050] in The polynomial representing the M+1th delay.

[0051] In step 3, the matrix It is expressed as:

[0052] ,

[0053] in represents the first term, first order filter coefficient; Represents the M+1th item, K+1th order filter coefficient.

[0054] Furthermore, the method of the present invention further comprises step 5: approximating the function by error The value of measures the performance of the variable fractional delay filter VFD;

[0055] Substitute the calculated filter coefficients into the following formula to obtain the error value, and plot the group delay and amplitude error with respect to the passband range respectively. , and the 3D graph of the delay p to observe the maximum error in group delay and amplitude:

[0056] ,

[0057] ,

[0058] ,

[0059] in represents the root mean square error, represents the maximum amplitude error in the filter passband, represents the maximum group delay error in the filter passband; Represents the frequency response of the designed fractional delay filter and the ideal fractional delay filter frequency response The difference between It can reflect the overall error amplitude of the filter passband; and are the group delay of the designed filter and the group delay of the ideal filter, respectively.

[0060] The present invention also provides an electronic device, comprising a processor and a memory, wherein the memory stores program code, and when the program code is executed by the processor, the processor executes the steps of the described method.

[0061] The present invention also provides a storage medium storing a computer program or instruction. When the computer program or instruction is run on a computer, the steps of the method described are executed.

[0062] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: 1. High precision and low calculation amount: Compared with the existing method for calculating VFD, the present invention adopts the least square method of one-time matrix inversion and performs QR decomposition on the matrix, which avoids mathematical operations such as partial derivatives and double integrals while ensuring the accuracy of group delay, reduces the complexity of coefficient solution, and improves the calculation efficiency of Farrow architecture variable fractional filter parameters;

[0063] 2. High design flexibility, suitable for broadband situations: Compared with the traditional method of designing non-adjustable filter parameters, the present invention uses an adjustable parameter filter to balance the filter stopband attenuation and transition band width, providing a more accurate frequency selection capability than the traditional method, especially in high-frequency conditions, it can obtain a relatively stable amplitude-frequency and phase-frequency characteristics. Compared with the existing weighted least squares method, the maximum amplitude error is reduced by 3.8dB, and the computational complexity is also reduced by an order of magnitude;

[0064] 3. Easy to implement in hardware: The calculated filter coefficients have complete symmetry, which is suitable for simulating the delay of different channels in parallel processing, and can save multiplication resources when implemented in FPGA. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is the basic architecture diagram of Farrow.

[0066] Figure 2 It is the amplitude-frequency response characteristic curve of the Farrow architecture filter.

[0067] Figure 3 It is the delay response characteristic curve of the Farrow architecture filter group.

[0068] Figure 4 It is the amplitude-frequency error response diagram of the Farrow architecture.

[0069] Figure 5 It is the Farrow architecture group delay error response graph. DETAILED DESCRIPTION

[0070] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, so that the above and other advantages of the present invention will become more clear.

[0071] In one embodiment of the present invention, a design method for a low-complexity, high-precision variable fractional delay filter is provided, comprising the following design steps:

[0072] Step 1: Implement the VFD filter using the Farrow architecture, such as Figure 1 The following is a diagram of the basic architecture of Farrow. Get the relevant parameters of the VFD filter, including the filter order K and the window function width factor , time delay p, normalized angular frequency of the filter , polynomial order R;

[0073] Step 2, according to the relevant parameters of the VFD filter, the sub-filter coefficient matrix is ​​pre-designed, and the sub-filter is designed by using an adjustable parameter window function. By adjusting the parameters, the frequency resolution of the VFD filter under different orders is adjusted, thereby reducing the Gibbs phenomenon without increasing the filter order;

[0074] Step 3, performing least square optimization solution according to the pre-designed sub-filter coefficient matrix, only one matrix inversion is required in the process of solving the coefficient; using QR decomposition matrix to avoid ill-conditioned matrix inversion problem, so as to obtain VFD filter coefficients with lower computational complexity, and fitting the coefficient matrix obtained by solution;

[0075] Step 4, according to the coefficient matrix obtained by fitting, it is applied to the Farrow architecture to obtain the coefficients of the VFD filter based on the Farrow architecture. The change of the delay amount does not require the change of the filter coefficient, which improves the calculation efficiency and storage space of the VFD filter.

[0076] In step 1, the frequency response of the variable fractional delay filter VFD can be derived from an actual filter impulse response:

[0077] A K-order finite impulse response can be expressed as:

[0078]

[0079] in is the coefficient of the k-th order filter, , K is the filter order; , intermediate parameters represents the filter passband range; is the discrete Fourier transform factor, j is the imaginary unit;

[0080] Under different delay conditions, Expressed as a function with delay p as the independent variable , use an R-order polynomial to fit, the expression is:

[0081]

[0082] in Represents the coefficient of the k-th order r-term sub-filter, r=0,1,…R; ;

[0083] Will Substitute the expression In the Farrow architecture, we get the transfer function :

[0084]

[0085] The polynomial coefficient frequency response , the factor matrix of the discrete Fourier transform , T represents matrix transpose; delay matrix vector , represents the time delay p of the filter from the 1st order to the R+1th order fitting polynomial; the polynomial coefficient matrix It is expressed as:

[0086] ,

[0087] Represents the coefficient matrix composed of R-term polynomial K-order sub-filters.

[0088] In step 2, according to the relevant parameters of the VFD filter, the sub-filter coefficient matrix is ​​pre-designed, and a Gaussian window function with adjustable parameters is selected. The Gaussian window function has a frequency domain smoothing characteristic, which can reduce the Gibbs phenomenon that occurs during the filter truncation process. According to the predetermined window function width factor, filter order, passband range, and delay, the sub-filter coefficient matrix is ​​obtained by the following formula:

[0089] ;

[0090] in is the Gaussian window function; It is an ideal impulse response. Only when the delay value p is an integer multiple of the sampling point n, The expression is not 0. When the delay value p is a fractional multiple of the sampling point, the ideal filter impulse response is an infinite non-causal sinc function, expressed as:

[0091] ;

[0092] is the Gaussian window function, The adjustable width factor of the window function is also the standard deviation of the Gaussian random variable. and Inversely proportional, the corresponding relationship is , is the index point of the current sample, ranging from , is the length of the window function, L=K+1. The formula is:

[0093] ,

[0094] Gaussian window function The value of depends on the filter order K. When K is low, increasing , the main lobe becomes wider, the frequency resolution is not high, but the side lobe performance is increased, the spectrum leakage is reduced, so that the filter can obtain relatively flat amplitude-frequency and phase-frequency characteristics without increasing the order; when K is high, the , the main lobe becomes narrower, the frequency resolution increases, and different frequency components can be accurately distinguished.

[0095] Here we calculate it by the formula The value is 1.2, the cutoff frequency Set to , 5th order polynomial fitting, delay range .

[0096] In step 3, the least square method is used, that is, the actual filter frequency response function is designed to approximate the ideal filter frequency response function, so as to optimize and minimize the error function. This is achieved through the following formula:

[0097]

[0098] Among them, through the frequency band , Multiply the error function by a non-negative weighting function , and integrate within the frequency band to obtain the optimized objective function In order to reduce the computational complexity, ; , , To calculate the filter coefficient correlation matrix. represents conjugation, is the frequency response of the actual filter of the Farrow architecture, is the frequency response of an ideal filter. , is the coefficient of the K-th order filter. Then the objective function Ask about The gradient of , the following expression is obtained through phase shift transformation:

[0099]

[0100] in , is the cosine function matrix, expressed as: , the filter coefficient solution involves The matrix inversion operation is performed, but this matrix is ​​independent of the delay parameter p, can be calculated in advance, and only needs to be calculated once. , is the real part operation, is the imaginary part operation, , are the real coefficient vector and imaginary coefficient vector of the actual filter coefficients, respectively. , .

[0101] Fit the filter coefficients to a polynomial:

[0102]

[0103] The different delays , , is the delay value. represents the first polynomial delay, Represents the M+1th polynomial delay; each delay corresponds to a polynomial, forming a polynomial delay matrix :

[0104] ,

[0105] in The polynomial representing the M+1th delay;

[0106] matrix It is expressed as:

[0107] ,

[0108] in , are the filter coefficients of the time delay polynomial, represents the first term, first order filter coefficient; represents the M+1th item, K+1th order filter coefficient;

[0109] The matrix Decompose into an upper triangular matrix and an orthogonal matrix The product of:

[0110]

[0111] Apply the coefficients solved by the least squares fit to the Farrow architecture:

[0112]

[0113] The matrix is the coefficient matrix of the Farrow architecture.

[0114] The coefficient matrix of the Farrow structure variable fractional-order delay filter is calculated by the above formula, so as to draw the amplitude-frequency and group delay characteristic curves of the Farrow architecture filter, as shown in Figure 2 The filter amplitude-frequency response characteristic curve is shown in Fig. Figure 3The figure shows the filter group delay response characteristic curve. The delay p value range is [0,0.5], with a step of 0.1, and five curves are drawn. The horizontal coordinates of the figure are all normalized frequencies. It can be seen that the windowing function combined with the least squares optimization method, when the filter order is low, the passband ripple fluctuation is small, fluctuating within the range of 0.015, and the group delay characteristic curve is also relatively flat. The simulation diagram shows that the windowing function combined with the least squares optimization method can obtain relatively flat passband amplitude-frequency and phase-frequency characteristics without increasing the VFD filter order.

[0115] The present invention also provides embodiment 2: When the VFD filter is applied to broadband conditions and the filter order is required to be relatively high, the filter order K is set to 70 and the cutoff frequency = , polynomial M=7, Take 0.02, delay range [-0.5, 0.5]. Through MATLAB simulation, the amplitude-frequency error and group delay error response diagrams under different fractional delays are obtained. Figure 4 The figure shows the amplitude-frequency error response of the Farrow architecture. Figure 5 The following is a graph showing the delay error response of the Farrow architecture group. Figure 4 It can be seen that the amplitude error of the VFD filter is mainly concentrated in -175~-120dB, represented by the yellow and red lines. Figure 5 The group delay error is kept at 10 -4 The maximum amplitude error and group delay error occur at the frequency Therefore, this method meets the broadband design requirements.

[0116] In order to evaluate the accuracy of the designed filter, some standards are defined to evaluate the filter performance, including the maximum root mean square error, the maximum amplitude error, and the maximum group delay error. Corresponding to the following formula:

[0117] Root mean square error ;

[0118] Maximum amplitude error ;

[0119] Maximum group delay error ;

[0120] Under the same conditions of K=70 and M=7, the design method of this embodiment is compared with the weighted least squares method and the linear optimization algorithm. The comparison table is shown in Table 1. It can be seen from the table that the maximum group delay error of the design method of the present invention is better than that of the weighted least squares method and the linear optimization method. The maximum error is low. Compared with the weighted least squares method, it is reduced by about 3.7dB, and the computational complexity is also reduced by an order of magnitude. It is an order of magnitude lower than the linear optimization algorithm and has a huge advantage in computational complexity.

[0121] From the above analysis, it can be concluded that the method of this embodiment can have a lower computational complexity while maintaining the high precision of the fractional delay filter.

[0122] Table 1

[0123]

[0124] The present invention provides a design method for a low-complexity, high-precision variable fractional delay filter. There are many methods and ways to implement the technical solution. The above is only a preferred implementation of the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims

1. A design method for a low-complexity, high-precision variable fractional delay filter, characterized in that: The following steps are involved: Step 1, using the Farrow architecture to implement a variable fractional delay filter VFD, and obtaining relevant parameters of the variable fractional delay filter VFD, wherein the relevant parameters include the filter order K, the window function width factor σ, the delay p, the normalized angular frequency ω of the filter, and the polynomial order R; Step 2, according to the relevant parameters of the variable fractional delay filter VFD, pre-design the sub-filter coefficient matrix, use the parameter-adjustable window function to design the sub-filter, and adjust the frequency resolution of the variable fractional delay filter VFD under different orders by adjusting the parameters; Step 3, performing least square optimization solution according to the sub-filter coefficient matrix, using QR decomposition matrix to obtain the coefficients of the variable fractional delay filter VFD with low computational complexity, and performing polynomial fitting on the coefficient matrix obtained by solving; Step 4, applying the coefficient matrix obtained by fitting to the Farrow architecture, thereby obtaining the coefficients of the variable fractional delay filter VFD based on the Farrow architecture; In step 3, the polynomial delay matrix D is expressed as: in The polynomial representing the M+1th delay; In step 3, the matrix H is expressed as: where h 0,0 represents the first term, first order filter coefficient; h M,K Represents the M+1th, K+1th order filter coefficient.

2. The method according to claim 1, characterized in that In step 1, the frequency response of the variable fractional delay filter VFD is derived from an actual filter impulse response, including: A K-order finite impulse response H(ω) is expressed as: where h k is the coefficient of the k-th order filter, k = 0, 1, ..., K, ω∈[0,bπ], and the intermediate parameter b∈[0,1] represents the passband range of the filter; e -jωk is the discrete Fourier transform factor, j is the imaginary unit; Under different delay conditions, h k It is expressed as a function h with delay p as the independent variable k (p), is fitted with an R-order polynomial, expressed as: Where c(k,r) represents the coefficient of the k-th order r-term sub-filter, r = 0, 1, ..., R; p ∈ [-0.5, 0.5]; h k (p) Substitute into the expression In the above equation, we get the transfer function H(ω,p) of the Farrow architecture: The polynomial coefficient frequency response The factor matrix of discrete Fourier transform a=[1,e -jw ,…,e -jwK ] T , T represents matrix transpose; delay matrix vector D = [1, p,…, p R ] T , represents the time delay p of the filter from the 1st order to the R+1th order fitting polynomial.

3. The method according to claim 2, characterized in that In step 1, the polynomial coefficient matrix C is expressed as: Where c(K,R) represents the coefficient matrix composed of R-term polynomial K-order sub-filters.

4. The method according to claim 3, characterized in that In step 2, the sub-filter coefficient matrix under different delay amounts is obtained by the following formula: h k (n)=h id (n-p)·w(n-p),0≤n≤K-1, where w(·) is the Gaussian window function; h id (n) is an ideal impulse response. Only when the delay value p is an integer multiple of the sampling point n, h id (n) The expression is not 0. When the delay value p is a fractional multiple of the sampling point, the ideal filter impulse response is an infinite non-causal sinc function, expressed as: h id (n)=sinc(n-p), The calculation formula of w(n) is: Where σ is the width factor of the window function, which is also the standard deviation of the Gaussian random variable. The intermediate parameter α is inversely proportional to σ, and the corresponding relationship is σ=(L-1) / 2α. L is the length of the window function, L=N+1.

5. The method according to claim 4, characterized in that In step 3, the least squares method is used, that is, the frequency response function of the actual filter is designed to approximate the frequency response function of the ideal filter and minimize the error function, which is achieved by the following formula: Among them, the optimization objective function J is obtained by multiplying the error function by a non-negative weighting function W(n) in the frequency band [0, bπ] and integrating it within the frequency band; P1, p1, p0 are the correlation matrices for calculating filter coefficients; [] * Indicates conjugation, H id (ω) is the frequency response of an ideal filter; Filter coefficient matrix h = [h(0), h(1), ..., h(K)] T , h(K) is the coefficient of the K-th order filter; Then find the gradient of the objective function J with respect to h, set J = 0, and obtain the following expression through transposition transformation: The matrix C1 is the cosine function matrix, expressed as: matrix Re(·) is the real part operation, Im(·) is the imaginary part operation, c1 and s1 are the real coefficient vector and imaginary coefficient vector of the actual filter coefficient respectively; c1=[1,cosω,…,cos(Kω)], s1=[0,sinω,…,sin(Kω)]; The obtained filter coefficients are fitted with a polynomial: DC T =H, Where D represents the polynomial delay matrix; H is the polynomial coefficient matrix corresponding to different delay amounts; Among them, different delays -0.5≤p0<…<p M <0.5, p0 represents the first polynomial delay, p M represents the M+1th polynomial delay; each delay corresponds to a polynomial, forming a polynomial delay matrix D; Decompose the matrix D into the product of an upper triangular matrix X and an orthogonal matrix Y, and we get: XYC T =H, Applying the coefficients obtained by the least squares fitting to the Farrow architecture yields: C=H T XY H 。 6. The method according to claim 5, characterized in that Also includes step 5: through the error approximation function E(ω) = |H(ω)-H id The value of (ω)| measures the performance of the variable fractional delay filter VFD; Substitute the calculated filter coefficients into the following formula to obtain the error value, and draw 3D graphs of group delay and amplitude error with respect to passband range ω and delay p to observe the maximum error of group delay and amplitude: e ∞ =20log 10 (max{|H(ω,p)-H id (ω,p)|, e g =max{|τ(ω,p)-τ id (ω,p)|}, Where ε2 represents the root mean square error, ε ∞ represents the maximum amplitude error in the filter passband, ε g represents the maximum group delay error in the filter passband; H(ω,p)-H id (ω,p) represents the designed fractional delay filter frequency response H(ω,p) and the ideal fractional delay filter frequency response H id (ω,p); τ(ω,p) and τ id (ω, p) are the group delay of the designed filter and the group delay of the ideal filter respectively.

7. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores program codes, and when the program codes are executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 6.

8. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is run on a computer, the steps of the method according to any one of claims 1 to 6 are executed.

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