An implementation method and device for obtaining an optimal FIR filter based on EVM calculation

Abstract

The application relates to the technical field of digital communication, and provides an implementation method for obtaining an optimal FIR filter based on EVM calculation. In the method, a low-pass FIR filter coefficient range is set, a P times sampling signal is obtained through sampling rate conversion and low-pass FIR filter filtering, wherein P is a natural number; EVM is calculated for the extracted sampling points; the optimal sampling point in the P times sampling signal is determined according to the calculated EVM result value; the corresponding system parameters and coefficient range of the FIR filter are found according to the optimal sampling point, so that the optimal FIR filter is determined. In the application, EVM is used as the evaluation function of the optimal filter, and the optimal filter coefficient under various constraint conditions can be quickly and accurately found. Especially for a system with limited hardware resources, the optimal filter can be obtained through setting different constraint conditions and floating point (fixed point) schemes.

Description

[Technical Field]

[0001] This invention relates to the field of digital communication technology, and in particular to a method and apparatus for obtaining the optimal FIR filter based on EVM calculation. [Background Technology]

[0002] Modern communication technologies are constantly evolving towards ultra-high speed, stability, and ultra-large capacity. In current high-speed fiber optic communication systems, high-order quadrature amplitude modulation (QAM) and high-bandwidth signals are widely used to improve system transmission rates. However, for high-bandwidth signals (greater than 60GHz), it is difficult to further increase the AD sampling rate. Optical communication typically uses a sampling rate that is 1.0 to 2.0 times the baud rate, requiring an additional upsampling stage for subsequent signal processing. Furthermore, the parallelism of AD sampling is generally 128 to 256. High-order modulation and high-parallelism sampling rate conversion filters place higher demands on performance and chip area. Therefore, a filter implementation method with the minimum area required to meet system requirements is needed.

[0003] Most current filter designs are based on approximating the minimum error or minimum mean square error of an ideal filter. What is obtained is usually the optimal solution of the ideal filter, but not necessarily the optimal solution of the communication system. [Summary of the Invention]

[0004] The technical problem this invention aims to solve is that traditional EVMs are generally used as a criterion for determining whether a communication transmission system can meet demodulation requirements, and are not used for filter design. Traditional filter implementation methods are generally based on window function methods, which are neither intuitive nor effective, and typically approximate ideal filters, resulting in poor performance for systems with limited hardware resources. Furthermore, some filter design methods based on polynomial methods have relatively fixed parameters, lacking versatility.

[0005] The present invention adopts the following technical solution:

[0006] A method for obtaining the optimal FIR filter based on EVM calculation includes: after setting the system parameters of the low-pass FIR filter, the method includes: setting the coefficient range of the low-pass FIR filter, and obtaining a signal with P times sampling by sampling rate transformation and low-pass FIR filter filtering; where P is a natural number; calculating EVM for the extracted sampling points, and determining the optimal sampling point in the P times sampling signal based on the calculated EVM result; and finding the corresponding system parameters and coefficient range of the FIR filter based on the optimal sampling point, thereby determining the optimal FIR filter.

[0007] Preferably, the EVM is calculated for the extracted sampling points, and the optimal sampling point in the P-fold sampled signal is determined based on the calculated EVM result value. Specifically, this includes: calculating P EVM result values ​​for each of the P-fold sampled signals, and taking the sampling signal corresponding to the smallest EVM result value as the optimal sampling point.

[0008] Preferably, when the low-pass FIR filter is specifically an N-point M-order low-pass filter, the specific details are as follows: The N-point M-order low-pass filter is described as follows: it is calculated using the formula Y[t]=D*C*X[tN / 2:t+N / 2]; where Y is the output result matrix with a size of 1×1; X[tN / 2:t+N / 2] is the sampling point of the random signal X_ref after modulation and ideal sampling rate transformation, which is the data sampled as Q before and after time t, with a size of N×1; D is the M-order fractional interpolation time matrix D=[d^M d^(M-1)d^(M-2)...d^0], with a size of 1×(M+1); C is the filter coefficient matrix with a size of (M+1)×N; d is the fractional interpolation time; the elements of the C coefficient matrix are adjusted to obtain the corresponding filter coefficients.

[0009] Preferably, it also includes: the fractional difference time d = mod(dt, 1); where dt = dt + step, dt = dt + step is executed once for each X input; step = 1 / (P / Q), where P is the sampling rate of X and Q is the sampling rate of Y.

[0010] Preferably, the calculation of EVM for the extracted sampling points specifically includes: using the formula Among them, P error The average power pow(Y_rx-X_ref,2) represents the error vector, where Y_rx is the optimal sampled signal of Y, and X_ref is a random signal; ref The average power pow(X_ref, 2) represents the ideal vector; the smaller the EVM, the closer the signal after sampling rate transformation is to the ideal signal, that is, the better the performance of the FIR filter.

[0011] Preferably, the system parameter settings for the FIR filter specifically include: setting the highest-order modulation scheme of the system;

[0012] Set the filter roll-off factor; set the preset sampling factor; set the filter order and fixed-point parameters.

[0013] Preferably, the highest-order modulation scheme of the system includes 16qam, 64qam or 256qam.

[0014] Preferably, α is the roll-off factor, which characterizes the degree of slow change in the system's amplitude-frequency response curve, where 0 < α < 1.

[0015] Preferably, the range of low-pass FIR filter coefficients is set as follows: the range of normalized coefficients of the low-pass FIR filter is set to [-1, 1].

[0016] Secondly, the present invention also provides a method for obtaining an optimal FIR filter based on EVM calculation, for implementing the method for obtaining an optimal FIR filter based on EVM calculation as described in the first aspect, the apparatus comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the processor to perform the method for obtaining an optimal FIR filter based on EVM calculation as described in the first aspect.

[0017] This invention uses the EVM as the evaluation function for the optimal filter, which can quickly and accurately find the optimal filter coefficients under various constraints. Especially for systems with limited hardware resources, the optimal filter can be obtained by setting different constraints and floating-point (fixed-point) conversion schemes. [Attached Image Description]

[0018] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments of the present invention will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0019] Figure 1 This is a flowchart illustrating an implementation method for obtaining the optimal FIR filter based on EVM calculation, provided by an embodiment of the present invention.

[0020] Figure 2 This is a flowchart illustrating an implementation method for obtaining the optimal FIR filter based on EVM calculation, provided by an embodiment of the present invention.

[0021] Figure 3 This is a schematic diagram illustrating the waveform shape effect of the roll-off factor according to an embodiment of the present invention;

[0022] Figure 4 This is a flowchart illustrating an implementation method for obtaining the optimal FIR filter based on EVM calculation, provided by an embodiment of the present invention.

[0023] Figure 5 This is a schematic diagram of a device for obtaining the optimal FIR filter based on EVM calculation, provided in an embodiment of the present invention.

Detailed Implementation Methods

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0025] In the description of this invention, the terms "inner", "outer", "longitudinal", "lateral", "upper", "lower", "top", "bottom", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and do not require that this invention must be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0026] Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0027] Example 1:

[0028] Embodiment 1 of this invention provides a method for obtaining the optimal FIR filter based on EVM calculation. After completing the system parameter settings of the low-pass FIR filter, as follows: Figure 1 As shown, the implementation methods include:

[0029] In step 201, the range of coefficients for the low-pass FIR filter is set, and after sampling rate transformation and filtering by the low-pass FIR filter, a signal with P times sampling is obtained; where P is a natural number.

[0030] For example, a 2x sampling rate means the sampling rate is twice the signal baud rate. This scheme is a filter design to implement sampling rate variation, which requires transforming the sampling rate to twice its normal value. Transforming it to twice its normal value facilitates EVM calculation; in actual implementation, other multiples can be used.

[0031] In step 202, the EVM is calculated for the extracted sampling points, and the optimal sampling point in the P-fold sampled signal is determined based on the calculated EVM result.

[0032] Specifically, based on the P times sampled signal, P EVM values ​​are calculated respectively, and the smallest EVM is taken as the optimal sampling point. The multiple of the sampled signal determines how many sets of sampled signals can be obtained for EVM calculation.

[0033] In step 203, the system parameters and coefficient range of the corresponding FIR filter are found based on the optimal sampling point, thereby determining the optimal FIR filter.

[0034] The smaller the EVM, the closer the signal after sampling rate transformation is to the ideal signal, indicating that the FIR filter has better performance.

[0035] This invention uses the EVM as the evaluation function for the optimal filter, which can quickly and accurately find the optimal filter coefficients under various constraints. Especially for systems with limited hardware resources, the optimal filter can be obtained by setting different constraints and floating-point (fixed-point) conversion schemes.

[0036] In conjunction with the embodiments of the present invention, there is also a preferred implementation scheme. The method for obtaining the optimal FIR filter based on EVM calculation, specifically when the low-pass FIR filter is an N-point M-order low-pass filter, where N and M affect the filter's order and coefficients, generally, a larger N results in better filter performance but also a greater computational load. Therefore, it is necessary to search for coefficients with different values ​​of N for practical system selection. In the embodiments of the present invention, a general calculation method is provided accordingly, specifically:

[0037] The N-point M-order low-pass filter is described as follows:

[0038] It is obtained by the formula Y[t]=D*C*X[tN / 2:t+N / 2];

[0039] Where Y is the output matrix, with a size of 1×1; X[tN / 2:t+N / 2] is the sampling point of the random signal X_ref (which is specifically represented as a random bit stream of 0s and 1s) after modulation and ideal sampling rate transformation, with a size of N×1, adjacent to the sampled data of Q before and after time t; D is the M-order fractional interpolation time matrix D=[d^M d^(M-1)d^(M-2)...d^0], with a size of 1×(M+1); C is the filter coefficient matrix, with a size of (M+1)×N; d is the fractional interpolation time; d=mod(dt,1), where mod means the modulo operation; dt=dt+step, where dt=dt+step is executed once for each X input; step=1 / (P / Q), where P is the sampling rate of X; and Q is the sampling rate of Y.

[0040] The elements of the C-coefficient matrix are adjusted to obtain the filter coefficients for the corresponding responses; the filter coefficients at all time points constitute the overall FIR filter coefficients. Specifically, the adjustment of the C-coefficient matrix elements is based on the fastest gradient descent method, with the EVM as the cost function, and the error value of the EVM serving as the basis for adjusting the C-coefficient matrix elements.

[0041] In conjunction with the embodiments of the present invention, a preferred implementation method is also provided for the calculation of EVM for the extracted sampling points involved in step 202, specifically including:

[0042] Through formula

[0043] Among them, P errorThe average power pow(Y_rx-X_ref,2) represents the error vector, where Y_rx is the optimal sampling point signal of Y (i.e., the output matrix); P ref The average power pow(X_ref, 2) represents the ideal vector. A smaller EVM indicates that the signal after sampling rate transformation is closer to the ideal signal, which means that the FIR filter has better performance. Among them, pow(Y_rx-X_ref, 2) is used to calculate the power, and its specific calculation method is pow(Y_rx-X_ref, 2) = (Y_rx-X_ref, 2) raised to the power of 2.

[0044] In conjunction with the embodiments of the present invention, the system parameter settings of the FIR filter involved in Embodiment 1 are as follows: Figure 2 As shown, it specifically includes:

[0045] In step 301, the highest-order modulation scheme of the system is set, such as 16qam, 64qam, or 256qam. The highest-order modulation indicates the highest requirements for the FIR filter. Here, qam stands for Quadrature Amplitude Modulation.

[0046] In step 302, the filter roll-off factor is set, and different roll-off factors correspond to different filter shapes.

[0047] In step 303, a preset sampling multiple is set, and different sampling multiples correspond to different passband frequencies and stopband frequencies.

[0048] In step 304, the filter order and fixed-point parameters are set, and the filter number N, order M, and different fixed-point parameters are set.

[0049] The low-pass FIR filter system parameters include the roll-off factor, which is a requirement of the communication system and affects the optimal filter coefficients. For example, α is the roll-off factor, representing the degree of slow change in the system's amplitude-frequency response curve, where 0 < α < 1. Figure 3 As shown, this diagram illustrates the filter shape effects exhibited by different roll-off coefficients.

[0050] In conjunction with embodiments of the present invention, there is a preferred implementation scheme in which the range of coefficients of the low-pass FIR filter is set, specifically as follows:

[0051] The normalized coefficients of the low-pass FIR filter are set to have elements in the C matrix ranging from [-1, 1], and the elements are real numbers.

[0052] Example 2:

[0053] Based on Embodiment 1, this invention provides a more complete implementation process for the method proposed in Embodiment 1, taking into account specific application scenarios and parameter settings. For example... Figure 4 As shown, it includes:

[0054] In step 401, system parameters are set, including:

[0055] (1) Set the highest order modulation mode of the system: 16, 64 or 256qam, etc. The highest order modulation indicates the highest requirements for the FIR filter.

[0056] (2) Set the system roll-off factor: Different roll-off factors correspond to different filter shapes.

[0057] (3) Set the required upsampling factor: Different upsampling factors correspond to different passband frequencies and stopband frequencies.

[0058] (4) Set the number of filter points N and order M and different fixed-point parameters.

[0059] (5) Other constraints.

[0060] Except for the FIR filter module that needs to be approximated, all other modules are ideal models.

[0061] In step 402, the FIR filter is set.

[0062] The normalization filter coefficients are set to a range of [-1, 1]. The FIR filter coefficients are initialized to all zeros. After sampling rate transformation and low-pass FIR filtering, a sampling signal with twice the compliance rate is obtained.

[0063] The convolution process for an N-point M-order filter can be described as follows:

[0064] Y = D * C * X

[0065] Where: (1)X is the input data matrix with a size of N×1, and Y is the output result matrix with a size of 1×1;

[0066] (2) D is the matrix of time d for M-order fractional interpolation, D = [d^M d^M-1d^M-2...d^0], with a size of 1×(M+1);

[0067] (3) C is the filter coefficient matrix: (M+1)×N;

[0068] In step 403, the optimal sampling point is extracted from the 2x sampled signal (select one from two), and the EVM is calculated.

[0069]

[0070] P error: Represents the average power of the error vector, P ref EVM represents the average power of the ideal vector. The smaller the EVM, the closer the signal after sampling rate transformation is to the ideal signal, which means that the FIR filter has better performance.

[0071] In step 404, the process of steps 401 to 403 is repeated to quickly approximate the minimum EVM using a linear programming problem (fastest gradient descent method). The minimum EVM represents the minimum error after the sampling rate transformation, and the filter coefficients are optimal at this time.

[0072] Since the embodiments of the present invention and Embodiment 1 are implementation schemes based on a common inventive concept, the description of the relevant technical details involved in Embodiment 1 is applicable to the embodiments of the present invention, and will not be repeated here.

[0073] Example 3:

[0074] Based on Embodiments 1 and 2 above, this embodiment also provides a preferred implementation scheme for obtaining the optimal FIR filter based on EVM calculation. In the method for obtaining the optimal FIR filter based on EVM calculation, when the low-pass FIR filter is specifically an N-point M-order low-pass filter, N and M affect the order and coefficients of the filter. Generally, the larger N is, the better the filter performance, but the greater the computational load. Therefore, it is necessary to search for coefficients with different values ​​of N for system selection in practice. In this embodiment of the invention, a general calculation method is provided accordingly, specifically:

[0075] The N-point M-order low-pass filter is described and calculated using the following formula:

[0076]

[0077] Where x is a symbol for the bit stream modulated according to a certain modulation format, which can be configured, such as MPSK, MQAM, etc. P f is the symbol sequence obtained by performing a P-fold upsampling operation on x, where the upsampling operation involves inserting P-1 zero values ​​between adjacent data. up This is the vector of upsampling filter coefficients, with a length of M+1. This filter can be a raised cosine filter, a square root raised cosine filter, or other filter coefficients.

[0078]

[0079] Where h t Let be the coefficient vector of the FIR filter at time t, i.e., the vector to be solved, with a length of L+1. This coefficient can be generated using the Matlab function `firls`, where the parameters can be configured according to actual needs.t Let be the symbol data to be processed at time t, with a sampling rate of P. Perform an upsampling operation I on the received data, where the upsampling operation inserts I-1 zero values ​​between adjacent data. The vector data at time t is of length I times the length of the upsampled data sequence, and has a length of L+1. z t The data at time t after filtering.

[0080] Define the cost function

[0081] Among them, for the sequence (sampling rate P·f) s Resampling is performed to obtain sequence z Q (sampling rate is Q·f) s Specifically, K = Q * I, which means for the sequence z from Starting from a position, data is extracted at certain intervals. The positions of the extracted data are spaced K apart. If the value of a position is not an integer, it is rounded to the nearest integer. To pass z Q The obtained reference symbol uses different hard decision methods for different modulation schemes, and the tuning method corresponds to x.

[0082] Set the initial value h of the filter coefficients. ini Given the range of filter coefficient values ​​and the number of iterations, and using J as the cost function, a linear programming algorithm is used to find the filter coefficient value h that minimizes J. opt .

[0083] In specific implementation scenarios, binary data streams can be mapped using a square 16QAM constellation to generate a sampling rate of f. s The 16QAM modulated symbol sequence is upsampled by 2 times and filtered by a raised cosine filter to obtain the sequence y, with a sampling rate of P = 2f. s The raised cosine filter has a roll-off factor of 0.1 and a length of 2049; its coefficients can be calculated using Matlab software. The sequence y is upsampled by a factor of 32, and then processed using a filter of length 257 to obtain the sequence z. To obtain the sampling rate... Data sequence, for sequence z according to from Starting from position 129, data is extracted. When the data position is not an integer, it is rounded. The rounded result is then processed to obtain sequence z. Q In order to obtain the reference sequence For z Q Make a hard decision. After obtaining z... Q as well as After sequencing, the EVM can be calculated. Using the optimal solution calculation method in Matlab, the EVM is set as the cost function, the number of iterations is 1000, and the filter coefficients are initialized to h. ini =firls(256,[00.0259 0.0369 1],[1 1 0 0]), the minimum value of the filter coefficients is firls(256,[0 1 / 64 1 / 64 1],[11 0 0]), and the maximum value is firls(256,[0 1 / 16 1 / 16 1],[1 1 0 0]). After 1000 iterations, the optimal solution h is obtained. opt =firls(256,[0 0.0237 0.0398 1],[1 1 0 0]).

[0084] Example 4:

[0085] like Figure 5 The diagram shown is an architectural schematic of a design device for obtaining the optimal FIR filter based on EVM calculation according to an embodiment of the present invention. The design device for obtaining the optimal FIR filter based on EVM calculation in this embodiment includes one or more processors 21 and a memory 22. Figure 5 Take a processor 21 as an example.

[0086] Processor 21 and memory 22 can be connected via a bus or other means. Figure 5 Taking the example of a connection between China and Israel via a bus.

[0087] The memory 22, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs and non-volatile computer-executable programs, such as the implementation method for obtaining the optimal FIR filter based on EVM calculation in Embodiment 1. The processor 21 executes the implementation method for obtaining the optimal FIR filter based on EVM calculation by running the non-volatile software program and instructions stored in the memory 22.

[0088] Memory 22 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some embodiments, memory 22 may optionally include memory remotely located relative to processor 21, which can be connected to processor 21 via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0089] The program instructions / modules are stored in the memory 22. When executed by one or more processors 21, they execute the implementation method for obtaining the optimal FIR filter based on EVM calculation in Embodiment 1 above. For example, they execute the above-described implementation method. Figure 1and Figure 2 The steps shown.

[0090] It is worth noting that the information interaction and execution process between the modules and units in the above-mentioned device and system are based on the same concept as the processing method embodiment of the present invention. For details, please refer to the description in the method embodiment of the present invention, and will not be repeated here.

[0091] Those skilled in the art will understand that all or part of the steps in the various methods of the embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, which may include: read-only memory (ROM), random access memory (RAM), magnetic disk or optical disk, etc.

[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An implementation method for obtaining an optimal FIR filter based on EVM calculation, characterized in that, After the system parameter setting of the low-pass FIR filter is completed, the implementation method comprises: Setting a low-pass FIR filter coefficient range, and obtaining a P times sampling signal through a sampling rate conversion and a low-pass FIR filter filtering; wherein, P is a natural number; Calculating an EVM for the extracted sampling points, and determining an optimal sampling point in the P times sampling signal according to the calculated EVM result value; According to the optimal sampling point, the corresponding FIR filter system parameters and coefficient range are searched, so as to determine the optimal FIR filter; When the low-pass FIR filter is a N-point M-order low-pass filter, the specific implementation is as follows: The N-point M-order low-pass filter is described as: The calculation is obtained through the formula Y[t]=D*C*X[t-N / 2:t+N / 2]; Wherein, Y is the output result matrix, the size is 1*1; X[t-N / 2:t+N / 2] is the adjacent sampling point of the data with a sampling rate of Q at t time after the random signal X_ref is modulated and ideal sampling rate conversion, the size is N*1; D is the M-order decimal interpolation time matrix D=[d^Md^(M-1)d^(M-2)...d^0], the size is 1*(M+1); C is the filter coefficient matrix, the size is (M+1)*N; d is the decimal interpolation time; Adjust the C coefficient matrix elements to obtain the corresponding response filter coefficient; The EVM is calculated for the extracted sampling points, and the specific implementation is as follows: By the formula wherein P error represents the average power of the error vector pow(Y_rx-X_ref,2), Y_rx is the optimal sampling point signal of Y, and X_ref is a random signal; P ref represents the average power of the ideal vector pow(X_ref,2); the smaller the EVM, the closer the signal after the sampling rate conversion is to the ideal signal, i.e., the better the performance of the FIR filter.

2. The implementation method for obtaining optimal FIR filter based on EVM calculation according to claim 1, characterized in that, The EVM is calculated for the extracted sampling points, and the specific implementation is as follows: According to the P times sampling signal, P EVM result values are calculated respectively, and the sampling signal corresponding to the smallest EVM result value is taken as the optimal sampling point.

3. The implementation method for obtaining optimal FIR filter based on EVM calculation according to claim 1, characterized in that, Also includes: The decimal difference value time d=mod(dt,1); Wherein, dt=dt+step, dt=dt+step is executed once for each X input; step=1 / (P / Q)P is the sampling rate of X; Q is the sampling rate of Y.

4. The implementation method for obtaining an optimal FIR filter based on EVM calculation according to any one of claims 1-3, characterized in that, The system parameter setting of the FIR filter comprises: Setting the modulation mode of the highest order of the system; Setting the filter roll-off coefficient; Setting the preset sampling multiple; Setting the order and fixed-point parameter of the filter.

5. The implementation method for obtaining an optimal FIR filter based on EVM calculation according to claim 4, characterized in that, The modulation mode of the highest order of the system comprises 16qam, 64qam or 256qam.

6. The implementation method for obtaining optimal FIR filter based on EVM calculation according to claim 4, characterized in that, Alpha is the roll-off coefficient, which represents the degree of slow change of the system amplitude-frequency characteristic curve, wherein 0<alpha<1.

7. The method of claim 1-3, wherein the method is based on EVM calculation to obtain the optimal FIR filter implementation. The low-pass FIR filter coefficient range is set, specifically: The low-pass FIR filter normalization coefficient range is set to [-1, 1].

8. An apparatus for obtaining the optimal FIR filter based on EVM calculation, characterized in that, The device comprises: At least one processor; and a memory connected in communication with the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the processor to execute the implementation method for obtaining the optimal FIR filter based on the EVM calculation according to any one of claims 1-7.

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