An Optimization Design Method for Variable Fractional Delay FIR Filters Based on Intelligent Optimization Algorithms

Abstract

A method for optimizing the design of a variable fractional delay (FIR) filter based on an intelligent optimization algorithm includes: S1 transforming the design problem of a Farrow structure FIR filter into solving two ill-conditioned linear equations; S2: using an improved principal component weighted iterative algorithm to solve the ill-conditioned linear equations, where the weighting factors of the principal component weighted algorithm are associated with the optimization parameters through an exponential mapping relationship; S3: constructing a collaborative optimization framework using the Runge-Kutta optimization algorithm, using the error norm of the filter coefficient vector solution as the optimization objective, and jointly optimizing the parameters and the filter order; iteratively solving the ill-conditioned linear equations to obtain the optimal sum of filter coefficients, thus completing the filter design. This invention overcomes the high computational complexity of traditional linear programming and second-order cone programming methods, and further optimizes the filter order while achieving the same performance, saving 28% of hardware resources.

Description

Technical Field

[0001] This invention relates to the field of digital signal processing technology, and in particular to a design method for a variable fractional delay filter. Background Technology

[0002] In digital signal processing, finite-length unit impulse response (FIR) filters are widely used due to their inherent stability and ability to achieve linear phase. As an important branch, variable fractional delay (VFD) filters can achieve continuously adjustable and precise signal delays beyond integer sampling periods, thus becoming a core device for solving problems related to clock synchronization, sampling rate conversion, and beamforming. VFD filters are widely used in modern communication systems, radar signal processing, multi-channel sampling synchronization, and high-precision audio processing to achieve finely continuous and adjustable signal delays.

[0003] The Farrow architecture is an efficient framework for implementing VFD filters. It achieves rapid online adjustment of the delay by expressing the filter coefficients as polynomials with respect to the fractional delay parameter. The core of VFD filter design lies in making its frequency response approximate the ideal amplitude response over the widest possible bandwidth, i.e., simultaneously and precisely controlling both the amplitude response and group delay response. Existing design methods can be mainly divided into two categories: time-domain interpolation methods and frequency-domain optimization methods. Time-domain interpolation methods (such as Lagrange and B-spline interpolation) are computationally simple, but they often exhibit significant amplitude attenuation and phase distortion at the high-frequency edges of the passband. Frequency-domain optimization methods directly minimize the error from the ideal response in the frequency domain, achieving superior overall performance.

[0004] In frequency domain optimization methods, linear programming (LP) and second-order cone programming (SOCP) transform the minimum-maximum error problem into a convex optimization model, ensuring global optimality of the solution and achieving extremely high design accuracy. These methods are considered benchmark methods for high-performance VFD filter design. However, the computational complexity of these methods is not only related to the filter order (variable dimension) but also heavily depends on the number of discrete grid points (constraints) set to approximate the continuous frequency domain. When pursuing high-precision design, the massive constraint set leads to an exponential increase in computational load and lengthy solution times, making them unsuitable for scenarios requiring frequent iterative design or real-time optimization.

[0005] To reduce computational complexity, the Principal Weighted Iteration (PEWI) algorithm has been introduced to solve ill-conditioned linear equations in VFD design. This algorithm has a simple iterative format, fast convergence speed, and its computational load depends only on the dimension of the coefficient vector to be solved, and is independent of the number of discrete points, thus exhibiting a significant efficiency advantage when dealing with high-density discretization problems. However, the convergence and performance of the PEWI algorithm are highly dependent on the selection of its weight parameters. The lack of a systematic selection criterion for these parameters, often relying on empirical trial and error, leads to insufficient convergence reliability and makes it difficult to consistently achieve optimal design results.

[0006] Furthermore, both traditional LP / SOCP methods and the PEWI algorithm typically fix the filter order during the design process. To find the minimum order that meets performance requirements and minimizes hardware resource consumption, designers must conduct multiple manual trial-and-error processes, which are tedious and cannot guarantee optimality. In recent years, although some research has attempted to use swarm intelligence algorithms (such as particle swarm optimization) for global optimization, these algorithms generally suffer from problems such as getting trapped in local optima and slow convergence speed when dealing with such high-dimensional and complex constraint optimization problems, and their overall performance often fails to surpass that of traditional methods.

[0007] Therefore, a new design method is needed that can synergistically optimize filter performance and filter order. It should inherit the high efficiency of the PEWI algorithm while overcoming its shortcomings in setting parameters, and fundamentally solve problems such as high computational complexity, inability to automatically optimize the structure, and susceptibility to local optima. Summary of the Invention

[0008] The technical problem to be solved by this invention is:

[0009] Existing variable fractional delay (VFD) filter design methods, especially linear programming (LP) and second-order cone programming (SOCP), while offering high design accuracy, suffer from extremely high computational complexity and lengthy solution times, making them unsuitable for scenarios requiring rapid iteration or real-time optimization. Furthermore, existing methods typically design with a fixed filter order, failing to automatically find the minimum order that meets performance requirements, thus hindering the coordinated optimization of filter performance and hardware resource consumption. In addition, although some efficient algorithms, such as principal component weighted iteration (PEWI), have been introduced to reduce computational load, their core parameters lack systematic optimization criteria, resulting in insufficient convergence reliability and unstable design performance.

[0010] Therefore, the present invention aims to provide a novel collaborative optimization design method for VFD filters to solve the problems of computational complexity, filter order optimization, and adaptive adjustment of algorithm parameters.

[0011] The technical solution of this invention is:

[0012] A collaborative optimization design method for variable fractional delay filters is proposed. Its core lies in constructing a hybrid optimization framework (RUN-IPEWI), which combines an improved principal component weighted iterative algorithm (IPEWI) with a Runge-Kutta optimization algorithm (RUN) to achieve simultaneous optimization of filter coefficients and filter order. This method transforms the design problem of odd-order Farrow structure variable fractional delay filters into a problem of solving ill-conditioned linear equations. An exponential mapping is introduced to improve the parameter search space of the principal component weighted iterative algorithm, significantly enhancing its convergence reliability. A collaborative optimization framework is established using an optimizer (RUN) based on Runge-Kutta numerical theory, with the infinite norm of the filter passband amplitude error and group delay error as the joint objective function. This simultaneously optimizes the parameters β and filter order of the IPEWI algorithm, thereby minimizing the filter order while satisfying performance constraints. Specifically, the method includes the following steps:

[0013] S1: The error of the Farrow structure variable fractional delay filter is decomposed into real and imaginary parts. The process of minimizing the error is transformed into solving two ill-conditioned linear equations. and ,in, F and G It is a matrix composed of discrete points of frequency and delay. and For the ideal delayed response vector, and Let be the filter coefficient vector to be solved;

[0014] S2: The ill-conditioned linear equation system is solved using an improved principal component weighted iterative algorithm. The weighting factor of the principal component weighted algorithm is... Through the exponential mapping relationship With optimization parameters Related, among which ;

[0015] S3: Construct a collaborative optimization framework using the Runge-Kutta optimization algorithm, with the error norm of the filter coefficient vector solution as the basis. and As the optimization objective, the optimization parameters Joint optimization is performed with the filter order; the optimized filter order and optimized parameters are then combined. The improved principal component weighted iterative algorithm is used to solve the ill-conditioned linear equations to obtain the optimal filter coefficients. and Complete the filter design.

[0016] Step S1 transforms the error minimization problem into a system of ill-conditioned linear equations, including: deriving the error function between the ideal frequency response and the actual frequency response of the filter, and resolving the real and imaginary parts of this error function at different frequencies. and delay Discrete sampling is performed within the interval to construct two independent ill-conditioned linear equation systems. Minimizing the errors of the real and imaginary parts is expressed as solving the ill-conditioned equation systems. For normalized angular frequency, parameters Used to specify the edge frequencies of the signal passband This represents a fractional delay of the sampling period.

[0017] S3: Construct a collaborative optimization framework using the Runge-Kutta optimization algorithm, with the error norm of the filter coefficient vector solution as the basis. and As the optimization objective, the optimization parameters Joint optimization is performed with the filter order; based on the optimized filter order and optimized parameters... The improved pivot element weighted iterative algorithm is used to solve the ill-conditioned linear equations to obtain the optimal filter coefficients. and Complete the filter design.

[0018] The step S1, which involves transforming the design problem into a system of ill-conditioned linear equations, includes:

[0019] In frequency and delay Discrete sampling is performed within the interval, and the problem of minimizing the real part error and the imaginary part error is respectively expressed as the ill-conditioned linear equation system.

[0020] The iterative format of the improved principal component weighted iterative algorithm described in step S2 is as follows:

[0021]

[0022] in, For the number of iterations, It is the identity matrix. For the algorithm's first The filter coefficient vector of the next iteration. For the algorithm's first The coefficient vector of the next iteration.

[0023] Step S3 optimizes the filter order, specifically:

[0024] The vector formed by the orders of the sub-filters of the VFD filter. and It is optimized as part of the decision variables of the Runge-Kutta optimization algorithm; Sub-filters in the Farrow structure The order of Sub-filter The order of the filter is determined. In the design, the sub-filters of the Farrow structure are divided into odd-numbered and even-numbered sub-filters based on coefficient symmetry. This represents the frequency response corresponding to an even-numbered sub-filter. This represents the frequency response corresponding to the odd-numbered sub-filters.

[0025] The decision variables of the Runge-Kutta optimization algorithm described in step S3 are defined as follows: and , For solving the system of imaginary equations The parameters of the IPEWI algorithm.

[0026] The beneficial effects of this invention are:

[0027] (1) This invention transforms the design problem of a variable fractional delay filter into an efficient problem of solving ill-conditioned equations and optimizing parameters through the RUN-IPEWI collaborative optimization framework. Its computation time is reduced by 84.38% and 99.00% compared with the traditional linear programming (LP) and second-order cone programming (SOCP) methods, respectively, achieving a leap from tens of minutes to several seconds, greatly shortening the filter design cycle and enabling it to be applied to scenarios that require frequent coefficient updates or rapid prototyping.

[0028] (2) This invention improves the parameter space of the PEWI algorithm through exponential mapping and combines it with the global search mechanism of the RUN algorithm, effectively solving the problems of difficult parameter setting and easy getting trapped in local optima in the original algorithm, and significantly improving the convergence reliability and consistency of the design process. The final designed filter maintains excellent filtering performance while minimizing hardware resources, and the total order of the sub-filters is reduced from 174 to 124, which can save 28% of hardware resources. Attached image description:

[0029] Figure 1 This is a diagram of the Faroe Islands structure.

[0030] Figure 2 This is an optimization flowchart for the RUN-IPEWI algorithm.

[0031] Figure 3 The iterative curve corresponding to the real part error of the optimized filter in the RUN-IPEWI algorithm.

[0032] Figure 4 The iterative curve corresponding to the imaginary part error of the optimized filter in the RUN-IPEWI algorithm is shown.

[0033] Figure 5 The image shows the response error of a variable fractional delay filter based on the RUN-IPEWI algorithm.

[0034] Figure 6 The diagram shows the group delay response error of the variable fractional delay filter based on the RUN-IPEWI algorithm.

[0035] Figure 7 The diagram shows the group delay response of a variable fractional delay filter based on the RUN-IPEWI algorithm. Detailed Implementation

[0036] Example:

[0037] For ease of description, the relevant technical terms appearing in the specific implementation method will be explained first.

[0038] FIR (Finite Impulse Response): Finite impulse response;

[0039] PEWI (Pivot Element Weighting Iterative): A pivot-weighted iterative algorithm.

[0040] In this embodiment, we verify the effectiveness of the above technical solution through simulation testing, including the following steps:

[0041] S1. Based on the odd-order Farrow structure, the error function between the ideal frequency response and the actual frequency response of the VFD filter is derived. The real and imaginary parts of this error function are discretized in the frequency domain and the fractional delay domain, respectively, to construct two independent ill-conditioned linear equation systems. and ,in and Here is the filter coefficient vector to be solved: and These are the ideal real-part delay response vector and the imaginary-part delay response vector, respectively. and These are the coefficient vectors of the even-numbered sub-filters and the coefficient vectors of the odd-numbered sub-filters, respectively, to be solved.

[0042] S1.1 Constructing the ideal frequency response of a variable fractional delay FIR filter :

[0043] (1)

[0044] Where j is the imaginary unit. For normalized angular frequency, parameters Used to specify the edge frequencies of the signal passband, in this embodiment Take 0.9, For width is frequency band, Here is the delay parameter, where The ideal VFD filter frequency response can be rewritten as:

[0045] (2)

[0046] in . This is an intermediate product in the derivation process, representing the part of the frequency response of an ideal VFD filter that is related to the adjustable parameter p.

[0047] S1.2, Derivation Actual frequency response of a layered variable fractional delay FIR filter :

[0048] Frequency response of the designed variable fractional delay FIR filter for:

[0049] (3)

[0050] (4)

[0051] in, Let be the unit impulse response sequence of the designed filter, where This indicates the half-order of the designed filter; the order of the designed filter is... The filter length is The impact sequence is expanded into M terms using a polynomial. A polynomial of degree M, Here, n represents the polynomial coefficients, n represents the nth impulse response sequence, m represents the mth polynomial term, and the maximum value of m is M. Then, the expression for the nth unit shock sequence is... The coefficient corresponding to the m-th power. The coefficient will vary as n and m change, so it is expressed as... Solving the problem using the proposed algorithm. Subsequently based on The sum of equation (4) can be obtained Impulse response with double sampling period delay The frequency response of the variable fractional delay FIR filter designed according to formulas (3) and (4) can be further divided into... Sub-filters.

[0052] (5)

[0053] in, , , and These represent rounding down and rounding up, respectively. for The m-th sub-filter, which is an even-degree polynomial, has (The subscript e indicates even-symmetric correlation) for The m-th sub-filter of odd-degree polynomial correlation has (The subscript o indicates odd symmetric correlation):

[0054] (6)

[0055] Due to sub-filters and The coefficients satisfy symmetry, that is

[0056] (7)

[0057] The symmetry of the sub-filter is due to m Decision, sub-filter It has even-symmetric parameters, while the sub-filter Having odd-symmetric parameters, the sub-filter can be further modified based on parameter symmetry.

[0058]

[0059] in

[0060] (8)

[0061] Therefore, the transfer function of the designed filter can be rewritten as:

[0062] (9)

[0063] in

[0064] (10)

[0065] Considering the case where each sub-filter has a different order, the frequency response of the sub-filter is:

[0066] (11)

[0067] in

[0068]

[0069] in, The m-th sub-filter is derived based on the system symmetry (subscript e indicates even symmetry) condition in (7). coefficient, The m-th sub-filter is derived based on the coefficient symmetry condition (subscript o indicates even symmetry) in (7). coefficient, and This is the coefficient vector composed of these coefficients. For the m-th sub-filter The sine vector obtained from it, For the m-th sub-filter The cosine vector obtained from this. Here To represent the even-symmetric coefficients of the first... m Sub-filters The order, also The first coefficient is odd-symmetric. m Sub-filters The order of.

[0070] therefore, It can be represented as:

[0071] (12)

[0072] in

[0073]

[0074] and Let be the filter coefficient vector that needs to be solved. It is a sine vector and a delay parameter The vector formed It is the cosine vector and the delay parameter The vector formed.

[0075] S1.3, Based on the ideal variable frequency response and actual variable frequency response The variable fractional delay response error of the variable fractional delay FIR filter is obtained as follows:

[0076] (13)

[0077] in

[0078] (14)

[0079] (15)

[0080] in, This represents the real part of the response error of the variable fractional delay FIR filter (the subscript R indicates the real part). This represents the imaginary part response error of the variable fractional delay FIR filter (the subscript I indicates the imaginary part). and These are the filter coefficients for the real and imaginary parts, respectively.

[0081] S1.4, Frequency band range and delay interval With step size and Discretize, Discretize into Points ( Indicates the first (frequency band point) Discretize into Points ( Indicates the first (delay points), to obtain grid points Establish a mapping relationship ( ),therefore Indicates the first There are grid points. Based on the mapping relationship, a one-to-one index mapping is performed on formulas (14) and (15) to obtain...

[0082] (16)

[0083] and

[0084] (17)

[0085] Where matrix F is derived from formula (14) Corresponding grid points The matrix obtained after mapping, each Corresponding to a vector , forming a row vector of matrix F, that is The mapping of root (14) can be obtained Similarly, formula (15) can be discretized to obtain matrix G and Based on the above mapping relationship, the following system of linear equations with full rank can be obtained:

[0086] (18)

[0087] (19)

[0088] in

[0089]

[0090] Equations (18) and (19) are approximations of continuous functions, and only approximate solutions exist. Further processing of these solutions (multiplying them by the transposes of matrices F and G) is required. and )have to:

[0091] (20)

[0092] (twenty one)

[0093] Equations (20) and (21) are ill-conditioned systems of equations, where vectors and These are the coefficients of the designed filter.

[0094] S2. The improved principal component weighted iterative (IPEWI) algorithm is used to solve the above ill-conditioned linear equation system. The improvement lies in the introduction of an exponential mapping. The weight parameters in the original PEWI algorithm that are difficult to optimize directly will be removed. Mapped to a new parameter that is easy to search for in the optimization algorithm. The spatial design significantly improves the adjustability and optimizability of the parameters, thereby enhancing the convergence reliability and stability of the algorithm.

[0095] S2.1, Taking the system of equations (20) as an example, for an ill-conditioned system of equations It introduces the following iteration format:

[0096] (twenty two)

[0097] As a weighting factor, the selection range is , The number of algorithm iterations. As the initial value for iteration, For the first The result of the next iteration.

[0098] Weighting factors in the PEWI algorithm The selection is very important, if Selecting too small a pair of matrices The improvement in pathological conditions is also minimal, and may even lead to unstable solution results. If Too large a selection The value will deviate significantly This results in a convergence speed that is too slow, or even fails to converge.

[0099] However, there is no standardized formula for the specific value of the weighting factor; it can only be found based on experience or numerical methods.

[0100] S2.2 For the above ill-conditioned linear equation systems (20) and (21), The PEWI algorithm converges over time, but different... The convergence speeds are different, and as... Decreasing the convergence speed also gradually accelerates the process. Because... For systems of equations with severe ill-conditioned problems, swarm intelligence optimization algorithms struggle to find weighting factors that allow PEWI to converge to a minimum. Therefore, we introduce the following exponential mapping to improve the swarm intelligence optimization algorithm's performance in such cases. Regarding the search capability, we only consider the optimal convergence interval here. ,Right now .

[0101] (twenty three)

[0102] Based on this mapping swarm intelligence optimization algorithm, it is possible to search... The optimal value is thus indirectly determined. The optimal value that allows PEWI to converge, and the optimized PEWI algorithm, is called the IPEWI algorithm.

[0103] S2.3, Substitute (23) into (22) and rewrite the iterative format of the improved principal component weighted iterative algorithm (IPEWI) as follows:

[0104] (twenty four)

[0105] make We can obtain:

[0106] (25)

[0107] in The error vector between the k-th and k+1-th iteration results is simplified to equation (13):

[0108] (26)

[0109] When the iteration sequence The algorithm stops iterating when it converges to a fixed value or reaches the maximum number of iterations, and returns the solution to the system of equations. According to formula (26) and Iterative solutions to the ill-conditioned equations (20) and (21) can be achieved, thereby minimizing the filter response error.

[0110] S3. A collaborative optimization framework is established using the Runge-Kutta-based optimization algorithm (RUN) as the global search mechanism. This framework uses the infinite norm of the filter's passband amplitude error and the infinite norm of its group delay error as joint optimization objectives, enabling the RUN algorithm to synchronously and automatically optimize the parameters of the IPEWI algorithm. And the order of the variable fractional delay filter. The RUN algorithm, through its inherent gradient-guided mechanism, effectively avoids the problem of traditional swarm intelligence algorithms getting trapped in local optima, thus efficiently finding the global optimum or near-optimal solution in a complex search space.

[0111] S3.1 The design objective of the variable fractional delay filter is transformed into a multi-objective optimization problem, the optimization objective of which is to simultaneously minimize the real part error infinity norm. and the infinite norm of the imaginary part error To simultaneously optimize the filter structure and performance, two sets of decision variables are defined. For the real part error equation system, the decision variables are:

[0112]

[0113] in, Sub-filters in the Farrow structure The order of For solving the system of equations with real parts The parameters of the IPEWI algorithm, for the imaginary part error equation system, have the following decision variables:

[0114]

[0115] in, Sub-filter The order of For solving the system of imaginary equations The parameters of the IPEWI algorithm.

[0116] S3.2 Cooperative Optimization Execution Based on Runge-Kutta Optimization Algorithm: The constructed optimization problem is solved using the Runge-Kutta optimization algorithm. This optimization process iteratively updates the population to find the optimal solution through the following mechanism: an initial population is randomly generated within the given decision variable boundaries. The elements (representing the filter order) of each individual in the population are rounded before fitness evaluation to meet physical implementation requirements.

[0117] by Taking the optimization of group filters as an example, for each individual in the population... Its fitness value Calculate according to the following procedure:

[0118] a) From The order vector of the sub-filter is obtained by analysis. and IPEWI parameters .

[0119] b) According to Construct a matrix from discrete grid points. sum vector .

[0120] c) with Using the parameters, run the IPEWI algorithm (its iterative formula is: Solve the system of linear equations to obtain the optimal coefficients.

[0121] d) Calculate the infinite norm error corresponding to this coefficient: Similarly, calculating individuals fitness value .

[0122] Runge-Kutta optimization guides the search using gradient approximation based on the Runge-Kutta formula. Its core search movement (...) () is defined by the following formula:

[0123] (27)

[0124] in, The gradient vector is calculated based on the current population distribution and fitness. This represents element-wise multiplication. The increment is calculated based on population decision variables. This mechanism effectively balances global exploration and local exploitation through deterministic gradient guidance.

[0125] In the design example, the fitness function and The filter needs to be initialized, and its initialization parameters are set as follows:

[0126] The corresponding Farrow structure variable fractional delay filter for this parameter is as follows: Figure 1 The number of iterations in the RUN algorithm Population size ,because There are 6 sub-filters, and the upper and lower bounds of the decision variables are set to...

[0127]

[0128] To ensure the designed filter meets performance requirements, the given maximum amplitude response absolute error is: The maximum absolute delay error is For a flowchart of the algorithm for optimizing the design of a variable fractional delay filter using the RUN-IPEWI algorithm, please refer to [link / reference]. Figure 2 The process of the RUN algorithm calling the IPEWI algorithm to solve for fitness in the diagram is represented by a light-colored line.

[0129] The optimal decision value obtained after optimization is:

[0130]

[0131]

[0132] See Figure 3 and Figure 4 , Figure 3 The curves of the RUN algorithm iterations are shown when optimizing the equations corresponding to the real part of the error sub-filter. Figure 4 The iterative curves for optimizing the sub-filter corresponding to the imaginary part error are shown. The curves indicate that the real and imaginary parts have essentially converged after 20 iterations. The parameter values ​​for the PEWI algorithm in the two optimization problems are... and The sum of the orders of all sub-filters is The maximum absolute amplitude error of the designed filter. The maximum delay response error is The design took 31.003078 seconds, while the same performance filters LP and SOCP took 198.383878 seconds and 3114.158475 seconds respectively, and the total order of the filter was 174.

[0133] See Figure 5 This figure shows the variable fractional response error plot based on RUN-IPEWI. The maximum variable fractional response error can be obtained as follows: See also Figure 6 The figure shows the group delay response error of the variable fractional delay filter based on the RUN-IPEWI optimized design, with a maximum variable fractional response error of... See also Figure 7 The figure shows the group delay response of the variable fractional delay filter based on the design.

[0134] In summary, this invention can effectively improve the performance of variable fractional delay FIR filters and simplify the design of variable fractional delay filters.

Claims

1. A method for optimization design of a variable fractional delay FIR filter based on an intelligent optimization algorithm, characterized in that, Includes the following steps: S1: the process of minimizing the error is converted into solving two ill-conditioned linear equations and wherein, F and G are matrices composed of frequency and delay discrete points, and are the transpose matrices of the matrices F and G , respectively, and are ideal real part delay response vectors and imaginary part delay response vectors, respectively, and are even sub-filter coefficient vectors and odd sub-filter coefficient vectors to be solved, respectively; S2: The ill-conditioned linear equation system is solved using an improved principal component weighted iterative algorithm. The weighting factor of the principal component weighted algorithm is... Through the exponential mapping relationship With optimization parameters Related, among which ; S3: Construct a collaborative optimization framework using the Runge-Kutta optimization algorithm, with the error norm of the filter coefficient vector solution as the basis. and As the optimization objective, the optimization parameters Joint optimization is performed with the filter order; the optimized filter order and optimized parameters are then combined. The improved principal component weighted iterative algorithm is used to solve the ill-conditioned linear equations to obtain the optimal filter coefficients. and Complete the filter design.

2. The method for optimizing and designing a variable fractional delay FIR filter based on an intelligent optimization algorithm according to claim 1, characterized in that, The process of minimizing the error in step S1 is transformed into solving two ill-conditioned linear equations, including: deriving the error function between the ideal frequency response and the actual frequency response of the filter, and resolving the real and imaginary parts of the error function at angular frequencies. and delay Discrete sampling is performed within the interval to construct two independent ill-conditioned linear equation systems. Minimizing the errors of the real and imaginary parts is expressed as solving the ill-conditioned equation systems. Angular frequency, These are parameters used to specify the edge frequencies of the angular frequency. This represents a fractional delay of the sampling period.

3. The method for optimizing and designing a variable fractional delay FIR filter based on an intelligent optimization algorithm according to claim 1 or 2, characterized in that, The iterative format of the improved principal component weighted iterative algorithm described in step S2 is as follows: ,in, For the number of iterations, It is the identity matrix. For the algorithm's first The filter coefficient vector of the next iteration. For the algorithm's first The coefficient vector of the next iteration.

4. The variable fractional delay FIR filter optimization design method based on intelligent optimization algorithm according to claim 1, characterized in that... Step S3 optimizes the filter order, specifically: The vector formed by the orders of the sub-filters of the variable fractional delay filter. and As part of the decision variables of the Runge-Kutta optimization algorithm, it is optimized, wherein The number of sub-filters is even. The number of odd-numbered sub-filters; For the even-numbered sub-filters in the Farrow structure The order of Odd-numbered sub-filters The order of.

5. The variable fractional delay FIR filter optimization design method based on intelligent optimization algorithm according to claim 4, characterized in that, The decision variables of the Runge-Kutta optimization algorithm described in step S3 are defined as follows: and , The parameters are for the improved principal component weighted iterative algorithm for even-numbered sub-filters. The parameters are for the improved principal component weighted iterative algorithm for odd-numbered sub-filters, used to solve the real part of the system of equations. and the system of imaginary equations .

Images