Neural Network-Based Design Method and System for Reconfigurable Digital Filters

Abstract

This invention provides a method and system for designing reconfigurable digital filters based on neural networks, relating to the field of neural network technology. First, a target filter response description containing desired frequency response curve information and time-domain response constraint information is received. This description is then input into a pre-trained reconfigurable filter neural network for direct structural parameter mapping, generating a filter structure description, including filter coefficient parameters and topological connection information. Next, filter response simulation verification is performed based on this filter structure description to calculate the actual filter response description, which is then compared with the target description to generate an error description. Finally, the internal parameters of the neural network are adaptively adjusted and optimized based on the error description, ensuring that the error between the actual response and the target response meets a preset standard. This invention enables rapid, flexible, and accurate design of digital filters, adapting to diverse needs and improving design efficiency.

Description

Technical Field

[0001] This invention relates to the field of neural network technology, and more specifically, to a method and system for designing reconfigurable digital filters based on neural networks. Background Technology

[0002] In the field of digital signal processing, digital filters play a crucial role and are widely used in communications, audio processing, image processing, and many other areas. Traditional digital filter design methods are usually based on specific mathematical models and algorithms, such as the design methods for finite impulse response (FIR) filters and infinite impulse response (IIR) filters. These methods require professionals with deep mathematical knowledge and filter design experience to meet specific frequency and time domain response requirements through complex calculations and multiple iterations.

[0003] However, with the increasing diversification and complexity of application scenarios, higher demands are being placed on the performance and flexibility of digital filters. Traditional design methods suffer from problems such as long design cycles and poor adaptability when facing rapidly changing requirements and diverse design goals. For example, when designing filters with different frequency response curves and time-domain response constraints, traditional methods often require complex calculations and design processes to be repeated, making it impossible to quickly and efficiently generate filter structures that meet the requirements. Summary of the Invention

[0004] In view of the aforementioned problems, and in conjunction with the first aspect of the present invention, embodiments of the present invention provide a method for designing reconfigurable digital filters based on neural networks, the method comprising: Receive a target filter response description, which includes desired frequency response curve information and time-domain response constraint information; The target filter response description is input into a pre-trained reconfigurable filter neural network. The reconfigurable filter neural network performs a direct structure parameter mapping operation on the target filter response description to generate a filter structure description of the reconfigurable digital filter corresponding to the target filter response description. The filter structure description includes filter coefficient parameter information and filter topology connection information. Based on the filter coefficient parameter information and filter topology connection information in the filter structure description, a filter response simulation verification operation is performed to calculate the actual filter response description of the reconfigurable digital filter under the current filter structure description. By comparing the target filter response description with the actual filter response description, a filter response error description is generated, which includes frequency domain response error information and time domain response error information. Based on the filter response error description, the internal parameters of the reconfigurable filter neural network are adaptively adjusted and optimized, and the network weight parameters of the reconfigurable filter neural network are updated so that the filter response error description between the actual filter response description corresponding to the filter structure description output by the reconfigurable filter neural network and the target filter response description meets the preset convergence criterion.

[0005] Furthermore, embodiments of the present invention also provide a reconfigurable digital filter design system based on neural networks, comprising: A processor; a machine-readable storage medium for storing machine-executable instructions of the processor; wherein the processor is configured to execute the above-described neural network-based reconfigurable digital filter design method by executing the machine-executable instructions.

[0006] In another aspect, embodiments of the present invention also provide a computer program product, the computer program product including machine-executable instructions, the machine-executable instructions being stored in a computer-readable storage medium, a processor of a computer device reading the machine-executable instructions from the computer-readable storage medium, the processor executing the machine-executable instructions, causing the computer device to execute the above-described neural network-based reconfigurable digital filter design method.

[0007] Based on the above, by receiving the target filter response description containing the desired frequency response curve information and time-domain response constraint information, and using a pre-trained reconfigurable filter neural network to perform direct structural parameter mapping operations on it, a filter structure description of the reconfigurable digital filter corresponding to the target filter response description can be quickly generated. This includes filter coefficient parameter information and filter topology connection information, greatly shortening the design cycle of the digital filter and improving design efficiency. Simultaneously, based on the generated filter structure description, a filter response simulation verification operation is performed to calculate the actual filter response description. By comparing the target filter response description with the actual filter response description, a filter response error description is generated. Then, based on this error description, the internal parameters of the reconfigurable filter neural network are adaptively adjusted and optimized, ensuring that the error between the final output filter structure description and the target filter response description meets the preset convergence criterion. This ensures that the designed reconfigurable digital filter can accurately meet diverse design goals, exhibiting high adaptability and flexibility, and effectively solving the limitations of traditional digital filter design methods when facing complex and changing requirements. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of the execution flow of the reconfigurable digital filter design method based on neural networks provided in an embodiment of the present invention.

[0009] Figure 2 This is a schematic diagram of exemplary hardware and software components of the reconfigurable digital filter design system based on neural networks provided in an embodiment of the present invention. Detailed Implementation

[0010] Figure 1 This is a flowchart illustrating a neural network-based reconfigurable digital filter design method according to an embodiment of the present invention, which will be described in detail below.

[0011] Step S110: Receive the target filter response description, which includes the desired frequency response curve information and time-domain response constraint information.

[0012] Taking the design of a low-pass filter for speech signal preprocessing as an example, this step achieves the acquisition and standardization of target performance parameters through a multimodal input interface. A 16-bit precision parameter buffer is initialized to store the filter design specifications input by the user, supporting both graphical interface and configuration file input methods. In the graphical interface, the user fills in key specifications in a dedicated parameter configuration panel; the configuration file must contain two primary fields: the corresponding frequency response and time-domain constraints. Upon receiving the input data, a data verification process is initiated. First, the parameter integrity is checked, ensuring that the number of sampling points for the frequency response curve is not less than the preset minimum sampling point threshold M. The time-domain constraint parameters include three necessary dimensions: overshoot amplitude, decay time, and group delay fluctuation. Next, data validity verification is performed, such as ensuring that the passband cutoff frequency is less than the stopband start frequency, and that both are within the range of 0 to the Nyquist frequency (half the sampling rate). For speech signal processing scenarios, the sampling rate is set to Fs, and the Nyquist frequency is fixed at Fs / 2. After successful verification, the parameters are converted to 32-bit floating-point format and stored in a shared memory area for subsequent use by the neural network module.

[0013] Step S111: Receive the desired filter performance indicators input by the user through the graphical interface or configuration file. The desired filter performance indicators include passband cutoff frequency information, stopband start frequency information, maximum allowable ripple amplitude information in the passband, and minimum required attenuation information in the stopband.

[0014] Design a dual-path input processing mechanism to meet different user habits. In the graphical interface input mode, the passband cutoff frequency is set by a slider, with a range from Fmin to Fmax and a step size of ΔF. The stopband start frequency slider is linked to the passband cutoff frequency, and its minimum value is the sum of the passband cutoff frequency and ΔFmin. The passband ripple and stopband attenuation can be selected from preset values or manually entered through a drop-down menu. The passband ripple range is Rmin - Rmax dB, and the stopband attenuation range is Amin - Amax dB. The configuration file input mode supports batch parameter import. The file structure contains four parameter items corresponding to the passband cutoff frequency, stopband start frequency, passband ripple, and stopband attenuation. After parsing the file, a range check is performed on each parameter. If the parameter value is non-standard, it is automatically adjusted to the closest standard value. All input parameters are converted to standardized units, with frequency in Hz and amplitude in dB, and stored in a floating-point array of length 4. Array indices 0 to 3 correspond to the passband cutoff frequency, stopband start frequency, passband ripple, and stopband attenuation respectively. This process ensures the standardization and consistency of input parameters, laying the foundation for subsequent generation of the frequency response curve.

[0015] Step S112: According to the desired filter performance指标, generate a continuous and smooth desired frequency response curve information through an interpolation algorithm. The desired frequency response curve information includes the desired amplitude value information corresponding to each frequency point within the range from zero frequency to the Nyquist frequency.

[0016] First, construct a frequency axis sampling sequence that starts from 0 and ends at Fs / 2. Generate N frequency points (N is the preset number of sampling points) using logarithmic uniform sampling. The sampling density in the passband and stopband transition regions is increased by K times (K is an integer greater than 1) to capture the details of the transition band. For each frequency point fi, determine the desired amplitude value according to the following logic: when fi ≤ the passband cutoff frequency, the desired amplitude value is 1; when fi ≥ the stopband start frequency, the desired amplitude value is 0; when the passband cutoff frequency < fi < the stopband start frequency, use linear interpolation calculation, and the formula is the desired amplitude value = 1 - (fi - the passband cutoff frequency) / (the stopband start frequency - the passband cutoff frequency). Calculate N amplitude values to form an initial frequency response sampling point set, and then perform cubic spline interpolation on this sampling point set to make the curve smoothly transition in the transition band region, finally generating a continuous desired frequency response curve. This process ensures the continuity and smoothness of the frequency response curve through reasonable sampling and interpolation methods, accurately reflecting the desired filter frequency characteristics.

[0017] Step S113: According to the time-domain requirements of the filter design scenario, receive the user-specified time-domain response constraint information. The time-domain response constraint information includes the maximum overshoot amplitude limit information of the impulse response, the time length limit information required for the impulse response energy to decay to a specified percentage, and the group delay fluctuation range limit information.

[0018] In the time-domain constraint configuration panel, the user inputs the maximum overshoot amplitude limit Po (dimensionless proportionality coefficient) of the impulse response, the time required for the impulse response energy to decay to the initial energy P% limit Td sampling periods (P is a preset percentage value), and the group delay fluctuation range limit ±Tg (unit: sampling period). These parameters are converted into structured data. The energy decay time is quantified by calculating the cumulative integral of the sum of squares of the impulse response sequence at the sampling point where the total energy P% is reached. The group delay fluctuation is represented by the difference between the maximum and minimum values ​​of the group delay function within the passband. The input time-domain parameters are validated for reasonableness, ensuring that Po is between 0 and Po_max (preset maximum overshoot ratio), Td is between Td_min and Td_max (preset time range), and Tg is between 0 and Tg_max (preset maximum group delay fluctuation). After successful validation, the time-domain constraint information is stored as a three-dimensional vector, with vector elements corresponding to the overshoot amplitude limit, energy decay time limit, and group delay fluctuation range limit, respectively.

[0019] Step S114: Perform frequency domain sampling point encryption on the desired frequency response curve information, automatically increase the sampling point density in the frequency band region where the frequency response changes drastically, and generate high-resolution desired frequency response sampling sequence information.

[0020] First, the derivative of the desired frequency response curve is calculated, and the magnitude of the absolute value of the derivative is used to determine the degree of frequency change. A derivative threshold Dth is set; when the absolute value of the derivative in a certain frequency range is greater than Dth, it is determined to be a region of drastic change. In the flat regions of the passband and stopband, the original sampling interval Δf is maintained; in the transition band region, the sampling interval is reduced to Δf / K (K is the encryption factor, dynamically adjusted according to the magnitude of the absolute value of the derivative; the larger the derivative, the larger the value of K, and the maximum value of K does not exceed Kmax). After encryption, M sampling points (M>N) are obtained, forming a high-resolution desired frequency response sampling sequence, with the sampling point coordinates denoted as (fi, A(fi)), where fi is the frequency point and A(fi) is the corresponding amplitude value. The encrypted sampling sequence is verified to ensure that the frequency interval between adjacent sampling points is not less than Δf_min (the preset minimum sampling interval) to avoid data redundancy. Through encryption, more detailed frequency response information is obtained in key frequency band regions, improving the accuracy of subsequent feature extraction.

[0021] Step S115: Perform time-domain parameter quantization on the time-domain response constraint information to convert the non-quantized constraint information into quantized constraint vector information with a specific numerical range.

[0022] The maximum overshoot limit Po of the impulse response, the energy decay time Td, and the group delay fluctuation range ±Tg are converted into a three-dimensional vector Vt=[Po, Td, Tg]. Po is calculated as the ratio of the peak value to the steady-state value of the impulse response, Td is obtained through the energy accumulation integral, and Tg is obtained through statistical analysis of the group delay function. Each element in the vector is normalized. Po and Tg are divided by their respective maximum allowable values, and Td is divided by the sampling rate to obtain the time in seconds before normalization, so that the value range of each element in the vector is within the interval [0, 1]. The normalization method adopts the min-max normalization method, and the normalized value is calculated for each element separately. The formula is: element normalized value = (original value of element - minimum value of element) / (maximum value of element - minimum value of element), where the minimum and maximum values ​​of the element are the preset allowable range of parameters. Quantization operation converts the time-domain constraint information into a vector with uniform dimensions, which is convenient for fusion processing with frequency response characteristics.

[0023] Step S116: Perform format alignment and splicing operations on the high-resolution desired frequency response sampling sequence information and the quantization constraint vector information to combine them into a target filter response description vector of a unified dimension.

[0024] The high-resolution desired frequency response sampling sequence contains M amplitude values, forming a vector Vf of dimension M; the quantization constraint vector Vt is a three-dimensional vector. Vf and Vt are concatenated sequentially to form a target filter response description vector Vd = [A(f1), A(f2), ..., A(fM), Po, Td, Tg] of dimension M+3. Before concatenation, Vf is normalized, mapping the amplitude value A(fi) to the interval [0, 1], consistent with the element range of Vt, ensuring uniformity of dimensions for all elements in the vector. The concatenated vector undergoes a dimension check to ensure the vector length is M+3. If the length does not match, an error message is returned and the sampling and quantization steps are re-executed. Format alignment and concatenation operations integrate frequency and time-domain information into a unified description vector.

[0025] Step S117: Perform a normalization and scaling operation on the target filter response description vector to generate a normalized target filter response description. Before inputting the normalized target filter response description into the reconfigurable filter neural network, perform a description integrity verification operation to check whether the target filter response description vector contains valid data and whether there is any missing data.

[0026] The target filter response description vector Vd is processed using a min-max normalization method. For each element vdj in the vector, vdj' = (vdj - min(Vd)) / (max(Vd) - min(Vd)) is calculated, where min(Vd) and max(Vd) are the minimum and maximum values ​​of vector Vd, respectively. The normalized vector is denoted as Vd'. Integrity verification is then performed, checking for NaN or infinity values ​​in Vd' and verifying that the vector length is M+3. If outliers or length mismatches are found, the verification fails. During verification, each element of the vector is traversed, and the validity of each element is judged to ensure that all elements are finite values ​​within the interval [0, 1]. Normalization and integrity verification ensure that the data input to the neural network has good distribution characteristics and integrity, improving the stability of network training and inference.

[0027] Step S118: When the description integrity verification operation passes, the target filter response description is sent to the reconfigurable filter neural network for subsequent direct structure parameter mapping operation; when the description integrity verification operation fails, the user is prompted with a message indicating that the data is missing or invalid, and the system waits to receive a complete and valid target filter response description again.

[0028] After successful verification, Vd' is encapsulated as a neural network input tensor of shape [1, M+3] and transmitted to the input layer of the reconfigurable filter neural network via the data interface. If verification fails, an error message is displayed on the graphical interface, specifically indicating the missing parameter or invalid numerical range, and the focus is positioned on the corresponding input field, awaiting the user's correction and resubmission. The error message includes the specific error type and location, helping the user quickly locate the problem. While waiting for the user to re-enter, the current parameter cache is maintained, and only the parts modified by the user are updated, improving interaction efficiency. This step ensures that the data input to the neural network is complete and valid.

[0029] Step S120: Input the target filter response description into the pre-trained reconfigurable filter neural network, and perform a direct structure parameter mapping operation on the target filter response description through the reconfigurable filter neural network to generate a filter structure description of the reconfigurable digital filter corresponding to the target filter response description. The filter structure description includes filter coefficient parameter information and filter topology connection relationship information.

[0030] The reconfigurable filter neural network employs an encoder-decoder architecture. The input is a normalized target filter response description vector Vd', and the output is a filter structure description. The network first extracts features from the input vector, capturing deep features of the frequency response and temporal constraints through multiple convolutional layers and residual blocks. Then, it splits into two parallel branches: coefficient generation and topology generation, outputting filter coefficient parameters and topological connections respectively. Finally, a structure combination module generates a complete filter structure description. The network is trained using supervised learning, employing a large number of labeled filter design samples containing the input target response description and corresponding output structure parameters. After training, the network can directly map the target response to the filter structure without manual intervention. This neural network architecture is rationally designed, effectively integrating frequency and temporal information to achieve a direct mapping from the target response to the filter structure.

[0031] Step S121: Perform multi-resolution frequency band decomposition on the desired frequency response curve information in the target filter response description, divide the continuous frequency response curve information into multiple frequency sub-band information with overlapping regions, and extract the sub-band amplitude spectrum envelope feature information and sub-band phase change trend feature information corresponding to each frequency sub-band information.

[0032] The high-resolution desired frequency response sampling sequence Vf is divided into K frequency sub-bands. The sub-band division follows an equal-Q value principle, meaning the ratio of the center frequency to the bandwidth of each sub-band is constant. The center frequency sequence is denoted as fc1, fc2, ..., fcK, where fc1 = 0.1 × Fs / 2, fcK = 0.9 × Fs / 2, and adjacent center frequencies satisfy fc(i+1) = fc(i) × 2^(1 / B), where B is the number of sub-bands per octave, with a value of 3. The bandwidth of each sub-band is Δfc(i) = fc(i) / Q, where Q is the quality factor, with a value of 10. The overlap rate between sub-bands is 50%, meaning the upper limit frequency of the i-th sub-band overlaps with the lower limit frequency of the (i+1)-th sub-band. For each sub-band, the amplitude spectrum envelope is extracted by applying a moving average filter to the amplitude sampling points within that sub-band, with a window length of 1 / 5 of the number of sampling points in the sub-band. The phase change trend is determined by linearly fitting the phase sequence, calculating the slope of the fitted line as the phase change rate, and simultaneously calculating the root mean square of the fitting residual as the phase fluctuation feature. Multi-resolution band decomposition can capture signal features at different frequency scales.

[0033] Step S1211: Apply a windowed Fourier transform operation to the desired frequency response curve information. Convolve the desired frequency response curve information through a set of analysis window functions with center frequencies distributed at fixed intervals and gradually increasing bandwidth to generate a set of time-frequency coefficient information with different time-frequency resolutions.

[0034] The Gaussian window function is used as the analysis window. The center frequencies of the window functions are evenly distributed from 0 to Fs / 2, and a total of L window functions are set, with the center frequency interval being Fs / (2L). The standard deviation σ(i) of each window function is proportional to the center frequency fc(i), that is, σ(i)=fc(i) / 5, ensuring that the bandwidth of the high-frequency window is greater than that of the low-frequency window. The convolution is performed on the desired frequency response curve A(f) and each window function g(i, f), and the time-frequency coefficient C(i, k)=∫A(f)g(i, f-fk)df is obtained, where fk is the frequency sampling point. The time-frequency coefficients form an L×M matrix, with the rows representing the window functions with different center frequencies and the columns representing the frequency sampling points. Through the above method, different frequency resolutions can be obtained in different frequency ranges, with high resolution in the low-frequency region and low resolution in the high-frequency region, which conforms to the characteristic that the human ear is more sensitive to low-frequency signals.

[0035] Step S1212: According to the amplitude distribution of the time-frequency coefficient information, identify the frequency bands with gentle amplitude changes and the transition frequency bands with drastic amplitude changes in the desired frequency response curve information, and generate frequency band characteristic classification information.

[0036] Calculate the variance of the amplitude of the time-frequency coefficient at each frequency sampling point. The variance calculation formula is Var(k)=E[C(i, k)^2]-(E[C(i, k)])^2, where E[·] represents the average value over all window functions. Set the variance threshold Vth. When Var(k)<Vth, it is determined that this frequency point belongs to the frequency band with gentle amplitude changes; when Var(k)≥Vth, it is determined as the transition frequency band. Combine the continuous gentle frequency bands into a large frequency band, and mark the transition frequency bands separately to generate a frequency band characteristic classification label array with the length of M, and each element takes a value of 0 (gentle) or 1 (transition). This classification result will be used for subsequent adaptive sub-band division to ensure that more sampling resources are allocated in the transition band region and improve the analysis accuracy of the key frequency bands.

[0037] Step S1213: Based on the frequency band characteristic classification information, allocate a wider frequency sub-band division width to the frequency bands with gentle amplitude changes and a narrower frequency sub-band division width to the transition frequency bands with drastic amplitude changes, and generate an adaptive frequency division scheme information.

[0038] For frequency bands marked as smooth, the subband width is set to Wp = Fs / (2K); for frequency bands marked as transitional, the subband width is set to Wt = Wp / 2. Starting from frequency 0, the subband width is allocated according to the characteristics of the current frequency band. When a point of change in frequency band characteristics is encountered, the subband width is adjusted and the subband boundary is recalculated. The coordinates of the subband boundary points are stored in the array B = [b0, b1, ..., bK], where b0 = 0, bK = Fs / 2, and the range of each subband i is [bi, bi+1], satisfying bi+1 - bi = Wp or Wt, depending on the frequency band characteristics of that interval. The above adaptive partitioning method can reduce the amount of computation and improve processing efficiency while ensuring frequency resolution, making the subband partitioning more consistent with the actual characteristics of the frequency response.

[0039] Step S1214: According to the adaptive frequency division scheme information, define a set of frequency band boundary points with overlapping regions on the frequency axis. The frequency band boundary points divide the continuous frequency response curve information into multiple frequency interval information with overlapping beginning and end parts.

[0040] The subband overlap rate is set to R=0.5, meaning the starting boundary of each subband precedes the starting boundary of the previous subband by R×W, where W is the width of the current subband. For example, if the boundary of the previous subband is [bi, bi+1] and its width is W, then the boundary of the current subband is [bi+R×W, bi+1+R×W]. This method ensures an R×W overlap between adjacent subbands, guaranteeing the continuity of frequency response features. The final K subband intervals are denoted as [B1s, B1e], [B2s, B2e], ..., [Bks, Bke], where B(i+1)s = Bis + R×W(i), and W(i) is the width of the i-th subband. This overlap avoids information loss at subband boundaries, improving the completeness and accuracy of feature extraction.

[0041] Step S1215: Within each frequency interval, extract the amplitude value sequence of the desired frequency response curve within that frequency interval to form the amplitude sub-band information corresponding to that frequency interval; within each frequency interval, extract the phase value sequence of the desired frequency response curve within that frequency interval to form the phase sub-band information corresponding to that frequency interval.

[0042] For the i-th subband [Bis, Bie], find all sampling points in the high-resolution sampling sequence that satisfy Bis ≤ fk ≤ Bie, and extract the amplitude values ​​A(fk) of these points to form the amplitude subband information Ai = [A1, A2, ..., Am], where m is the number of sampling points in this subband. The phase value is obtained by performing a Hilbert transform on the frequency response curve, denoted as φ(fk), and similarly, the phase value in this subband is extracted to form the phase subband information Φi = [φ1, φ2, ..., φm]. If the number of sampling points in a subband is less than a preset threshold m0, its length is unified to m0 through zero padding or interpolation to ensure that the length of each subband information is consistent. This step decomposes the continuous frequency response curve into multiple subbands, preparing for subsequent feature extraction and analysis, so that the features of each subband can be processed independently.

[0043] Step S1216: Perform envelope extraction on each amplitude sub-band information, remove high-frequency fluctuation components from the amplitude sub-band information by low-pass filtering to obtain smooth amplitude sub-band envelope information, which serves as the sub-band amplitude spectrum envelope feature information; perform trend analysis on each phase sub-band information, fit the slope of the straight line of phase sub-band information with frequency using linear regression, use the slope of the straight line as the average phase change rate information of the sub-band, and calculate the residual fluctuation information of the phase sub-band information relative to the fitted straight line, which together constitute the sub-band phase change trend feature information.

[0044] Amplitude subband envelope extraction employs a moving average filter with a window length of m0 / 5 to filter the amplitude subband information Ai, yielding a smooth envelope Ei = [e1, e2, ..., em0]. In phase trend analysis, frequency point fk is used as the independent variable, and phase value φk is used as the dependent variable, performing a linear regression φk = a × fk + b, where the slope a is the average phase change rate. Residual fluctuation information is obtained by calculating the root mean square value of the residual sequence rk = φk - (a × fk + b), denoted as σφ. Subband phase change trend characteristics are represented as Pi = [a, σφ]. Through envelope extraction and trend analysis, the overall characteristics of the subband can be captured, noise interference can be removed, and the robustness of the features can be improved.

[0045] Step S1217: Combine the sub-band amplitude spectrum envelope feature information and sub-band phase change trend feature information corresponding to each frequency interval to form a complete representation of the frequency sub-band information. Arrange all the complete representations of the frequency sub-band information in order from low to high frequency to form the multi-resolution frequency band decomposition result of the frequency response curve information expected in the target filter response description.

[0046] Each frequency sub-band information is represented as Si = [Ei, Pi], where Ei is an m0-dimensional amplitude envelope vector and Pi is a 2-dimensional phase trend vector. Arranging the K sub-band information in ascending order of center frequency yields the multi-resolution frequency band decomposition result S = [S1, S2, ..., SK]. This multi-resolution frequency band decomposition result is a K×(m0+2) matrix, which serves as the input for subsequent feature fusion. Multi-resolution decomposition can capture signal features at different frequency scales, improving the neural network's ability to model frequency responses and enabling the network to better understand the characteristics and requirements of different frequency bands.

[0047] Step S122: Perform time-domain feature encoding on the time-domain response constraint information in the target filter response description, and convert the energy decay rate constraint information and group delay fluctuation constraint information of the time-domain impulse response into time-domain constraint feature vector information.

[0048] The time-domain response constraint information includes the energy decay rate and group delay fluctuation. The energy decay rate is represented by the half-life Td of the impulse response sequence, and the group delay fluctuation is represented by the standard deviation σg of the group delay function. Principal component analysis (PCA) is used for time-domain feature encoding to map the original time-domain constraint parameters to a low-dimensional space. First, a time-domain constraint parameter matrix containing a large number of samples is constructed, with each row representing the Td and σg of a sample. Dimensionality reduction using PCA yields two principal components. The current time-domain constraint parameters are projected onto these two principal components to obtain a 2D time-domain constraint feature vector Vt_enc=[c1, c2], where c1 and c2 are projection coefficients. This dimensionality reduction operation reduces the dimensionality of the time-domain features, lowers the computational complexity of subsequent feature fusion, and preserves the key information of the time-domain constraints.

[0049] Step S123: Perform cross-domain feature fusion operation on the sub-band amplitude spectrum envelope feature information, sub-band phase change trend feature information and time-domain constraint feature vector information corresponding to each frequency sub-band information to generate the fused intermediate representation information of the filter design target.

[0050] The multi-resolution frequency band decomposition result S is expanded into a one-dimensional vector of length K×(m0+2), denoted as Vf_enc. The temporal constraint feature vector Vt_enc is a two-dimensional vector. The two are concatenated along the feature dimension to obtain the fused vector Vfuse=[Vf_enc, Vt_enc], with a length of K×(m0+2)+2. To enhance the correlation of cross-domain features, the concatenated vector is processed by a multilayer perceptron. The perceptron contains two hidden layers. The first layer has half the length of the fused vector and uses ReLU as the activation function. The second layer has one-quarter the length of the fused vector, and its output serves as the intermediate representation information Vmid for the filter design target, with a length of K×(m0+2) / 4+0.5. Cross-domain fusion can organically combine frequency and temporal features, providing the neural network with more comprehensive design target information, enabling the network to comprehensively consider the requirements of both the frequency and temporal domains when designing filters.

[0051] Step S124: Input the intermediate representation information of the filter design target into the deep feature transformation module of the reconfigurable filter neural network, and perform nonlinear feature transformation operation on the intermediate representation information of the filter design target through multiple cascaded residual transformation layers, abstracting and generating high-dimensional filter design feature information layer by layer.

[0052] The deep feature transformation module comprises four residual transformation layers, each consisting of a convolutional layer, a batch normalization layer, and a ReLU activation function. The first residual layer takes Vmid as input, has a 3×3 kernel, and outputs 256 channels; the second, third, and fourth have the same kernel size and output 512 channels. Each residual layer includes a skip connection, directly adding the input to the convolutional layer output before passing it through the activation function. After processing by these four residual layers, the output feature map is flattened into a one-dimensional vector, serving as the high-dimensional filter design feature information Vhigh, with a length of 256×H×W, where H and W are the height and width of the output feature map from the last residual layer. Deep feature transformation maps intermediate representations to a higher-dimensional feature space through nonlinear transformations, capturing more abstract filter design principles.

[0053] Step S125: Input the high-dimensional filter design feature information into the coefficient generation branch of the reconfigurable filter neural network, and process it through a fully connected layer and activation function to directly map and generate the filter coefficient parameter information of the reconfigurable digital filter. The filter coefficient parameter information includes the filter numerator polynomial coefficient sequence information and the filter denominator polynomial coefficient sequence information.

[0054] The coefficient generation branch includes 3 fully connected layers. The input of the first layer is Vhigh, the number of neurons is 1024, and the activation function is ReLU. The number of neurons in the second layer is 512, and the activation function is ReLU. The number of neurons in the third layer is 2×Nc, where Nc is the filter order. The output is divided into two parts. The first Nc neurons are the coefficients of the numerator polynomial, and the last Nc neurons are the coefficients of the denominator polynomial. To ensure that the leading coefficient of the denominator polynomial is 1, the denominator coefficients are normalized. That is, for the denominator coefficient sequence d = [d0, d1, …, d(Nc - 1)], after normalization, it becomes d' = [1, d1 / d0, d2 / d0, …, d(Nc - 1) / d0]. The numerator coefficient sequence m = [m0, m1, …, m(Nc - 1)] remains unchanged. Finally, the filter coefficient parameter information is represented as C = [m, d']. The coefficient generation branch directly maps to the filter coefficients through fully connected layers, avoiding the complex optimization process in traditional design methods and improving the design efficiency.

[0055] Step S126: Input the high-dimensional filter design feature information into the topology generation branch of the reconfigurable filter neural network simultaneously. Through the topology structure decoder, perform a topology relationship reasoning operation on the high-dimensional filter design feature information to generate the filter topology connection relationship information of the reconfigurable digital filter. The filter topology connection relationship information includes the connection graph information between filter basic units and the feedback path position information.

[0056] The topology generation branch uses a graph neural network decoder. The input is Vhigh. First, it is mapped to a node feature vector through a fully connected layer. The number of nodes is fixed at M, and each node represents a filter basic unit (such as an adder, a multiplier, a delay unit). Then, the attention weights between nodes are calculated through the graph attention layer. The connections with weight values greater than the threshold T are retained to form an adjacency matrix A, where A(i, j) = 1 indicates that there is a connection between node i and node j, and A(i, j) = 0 indicates no connection. The feedback path position is determined by detecting the cyclic paths in the adjacency matrix. If there exist i < j and A(j, i) = 1, it is determined as a feedback path, and the starting and ending node numbers of the path are recorded. Finally, the topology connection relationship information is represented as G = [list of node types, adjacency matrix, list of feedback paths]. The topology generation branch can automatically infer the filter topology structure based on high-dimensional features, realize the reconfigurable design of the filter, and increase the flexibility and adaptability of filter design.

[0057] Step S127: Perform a structural parameter combination and encapsulation operation on the filter coefficient parameter information output by the coefficient generation branch of the reconfigurable filter neural network and the filter topology connection relationship information output by the topology generation branch of the reconfigurable filter neural network to generate the filter structure description of the complete reconfigurable digital filter.

[0058] The filter coefficient parameter information C and topology connection information G are combined into structured data and encapsulated using a specified format. The specific structure includes a coefficient part and a topology part. The coefficient part contains numerator and denominator polynomial coefficients, and the topology part contains a list of node types, an adjacency matrix, and a list of feedback paths. During the encapsulation process, a consistency check is performed on the coefficients and topology relationships to ensure that the number of coefficients matches the number of multipliers in the topology and that the number of feedback paths does not exceed a preset maximum value. This structural parameter combination encapsulation integrates coefficient and topology information into a unified structural description, facilitating subsequent simulation verification and implementation, and ensuring the integrity and consistency of the filter structure.

[0059] Step S128: Using the filter coefficient parameter information and filter topology connection relationship information in the filter structure description of the reconfigurable digital filter, perform a filter structure syntax rule check operation to verify the logical matching status between the filter coefficient parameter information and the filter topology connection relationship information, and generate a structure validity flag.

[0060] The syntax rule checks include: 1) whether the first term of the coefficient d' of the denominator polynomial is 1; 2) whether the lengths of the coefficients in the numerator and denominator are equal; 3) whether the adjacency matrix A is a square matrix and its dimensions match the number of nodes; 4) whether the feedback path forms a closed-loop system; and 5) whether all multiplier nodes have been assigned coefficients. If the checks pass, a structure validity flag (Flag=1) is generated; otherwise, Flag=0, and the specific error type is recorded, such as "the first coefficient of the denominator is not 1" or "the number of nodes does not match the dimensions of the adjacency matrix." The structure syntax rule checks ensure that the generated filter structure is physically implementable, avoiding logical contradictions.

[0061] Step S129: When the structure validity flag indicates that the structure is valid, output the filter structure description of the reconfigurable digital filter to the filter response simulation verification operation step; when the structure validity flag indicates that the structure is invalid, trigger the remapping operation of the reconfigurable filter neural network, adjust the nonlinear feature transformation operation path of the deep feature transformation module in the reconfigurable filter neural network, and regenerate the filter structure description of the reconfigurable digital filter.

[0062] If Flag=1, the encapsulated filter structure description is sent to the simulation verification module; if Flag=0, the parameters of the deep feature transformation module are adjusted according to the error type. For example, when the first term of the denominator coefficient is incorrect, a gradient penalty term for the corresponding residual layer is added, and then steps S124 to S128 are re-executed until the structure validity flag is 1 or the maximum number of remapping operations is reached. The maximum number of remapping operations is set to 5. If it is still invalid, an error message is output and the process is terminated. The remapping operation can automatically correct errors in the structure generation process, improve the robustness of the system, and ensure the generation of a valid filter structure.

[0063] Step S130: Based on the filter coefficient parameter information and filter topology connection information in the filter structure description, perform filter response simulation verification operation to calculate the actual filter response description of the reconfigurable digital filter under the current filter structure description.

[0064] The actual operation of the filter is simulated using software simulation. A standard test signal is input, and the output response is calculated to evaluate the filter's performance. Using a unit impulse signal as input, the impulse response is obtained through time-domain simulation, and the frequency response is obtained through Fourier transform. Key features are extracted to form a description of the actual filter response. Simulation verification can objectively evaluate the filter's actual performance, provide feedback for neural network parameter optimization, and ensure that the designed filter meets the expected performance indicators.

[0065] Step S131: Based on the filter coefficient parameter information in the filter structure description, including the filter numerator polynomial coefficient sequence information and the filter denominator polynomial coefficient sequence information, construct the mathematical expression information of the difference equation of the reconfigurable digital filter.

[0066] The numerator polynomial coefficients m = [m0, m1, ..., m(Nc-1)] and denominator polynomial coefficients d' = [1, d1, d2, ..., d(Nc-1)] are analyzed from the filter coefficient parameter information. Based on the standard difference equation form of the digital filter, the difference equation is constructed as: y(n) = m0x(n) + m1x(n-1) + ... + m(Nc-1)x(n-Nc+1) - d1y(n-1) - d2y(n-2) - ... - d(Nc-1)y(n-Nc+1), where x(n) is the input signal, y(n) is the output signal, and n is the discrete-time index. The difference equation is the mathematical description of the filter's time-domain characteristics and is the foundation for time-domain simulation. Accurately constructing the difference equation is crucial for subsequent simulation verification.

[0067] Step S1311: Parse the filter numerator polynomial coefficient sequence information from the filter coefficient parameter information. The filter numerator polynomial coefficient sequence information is a sequence containing multiple real or complex values. Each value in the sequence represents the coefficient of different delay terms of the input signal in the difference equation.

[0068] The numerator polynomial coefficient array is extracted from the coefficient part by the parser, resulting in a numerator polynomial coefficient sequence m. The array length is Nc, and each element is a floating-point number representing the coefficient of the input signal x(nk), k=0,1,…,Nc-1. For example, m[0] corresponds to the coefficient of x(n), m[1] corresponds to the coefficient of x(n-1), and so on. The numerator coefficients determine the weighting method of the input signal by the filter, directly affecting the frequency response and time-domain characteristics of the filter.

[0069] Step S1312: Parse the filter denominator polynomial coefficient sequence information from the filter coefficient parameter information. The filter denominator polynomial coefficient sequence information is a sequence containing multiple real or complex values. The first value in the sequence is set to one, and the subsequent values ​​represent the coefficients of different delay terms of the output signal in the difference equation.

[0070] Extract the denominator polynomial coefficient array from the coefficient part to obtain the denominator polynomial coefficient sequence d', with an array length of Nc. The first element is fixed at 1, and the subsequent elements d'[1], d'[2], ..., d'[Nc-1] are the coefficients of the output signal y(nk), k=1, 2, ..., Nc-1. The denominator coefficients determine the feedback characteristics of the filter and have an important influence on the stability and frequency response of the filter. Their values ​​are directly related to whether the filter is stable and the shape of the frequency response.

[0071] Step S1313: Arrange the coefficients in the filter numerator polynomial coefficient sequence information in order of delay order from low to high to form the mathematical expression information of the numerator polynomial of the difference equation of the reconfigurable digital filter.

[0072] The numerator polynomial is mathematically expressed as M(z) = m0 + m1z^(-1) + m2z^(-2) + ... + m(Nc-1)z^(-(Nc-1)), where z^(-k) represents the unit delay operator with a delay of k sampling periods. The numerator polynomial reflects the forward filtering characteristics of the filter on the input signal, and the magnitude and sign of its coefficients determine the degree of amplification or attenuation of different frequency components by the filter.

[0073] Step S1314: Arrange the coefficients in the filter denominator polynomial coefficient sequence information in order of delay order from low to high to form the mathematical expression information of the denominator polynomial of the difference equation of the reconfigurable digital filter.

[0074] The mathematical expression of the denominator polynomial is D(z) = 1 + d1z^(-1) + d2z^(-2) + ... + d(Nc-1)z^(-(Nc-1)). The denominator polynomial reflects the feedback characteristics of the filter, and the distribution of its roots determines the stability of the filter. The filter is stable when the roots are inside the unit circle, otherwise it is unstable.

[0075] Step S1315: Based on the standard form of the difference equation of the digital filter, using the mathematical expression information of the numerator polynomial and the mathematical expression information of the denominator polynomial, write the input-output relationship in the form of discrete time series. The output of this input-output relationship is the mathematical expression information of the difference equation of the reconfigurable digital filter.

[0076] The mathematical expression of the difference equation is y(n) = (M(z) / D(z))x(n), which expands to a recurrence relation in the time domain: y(n) = sum_{k=0}^{Nc-1}m(k)x(nk) - sum_{k=1}^{Nc-1}d'(k)y(nk), where sum represents the summation operation. This difference equation describes the input-output relationship of the filter in the time domain and is the foundation for time-domain simulation. By solving this equation, the output response of the filter under different input signals can be obtained.

[0077] Step S1316: Verify whether the mathematical expression of the difference equation of the reconfigurable digital filter satisfies the causal system condition, and check whether the coefficient of the constant term in the mathematical expression of the denominator polynomial is zero.

[0078] Causal systems require that the constant term of the denominator polynomial be non-zero, i.e., the coefficient of the constant term d'(0) of D(z) = 1 ≠ 0. Therefore, this condition is automatically satisfied without additional adjustment. Causality is a fundamental condition for the physical realization of filters, ensuring that the system output depends only on the current and past inputs, which meets the needs of practical applications.

[0079] Step S1317: When the constant term coefficient of the denominator polynomial mathematical expression information is not zero, the difference equation mathematical expression information of the reconfigurable digital filter is considered causal and realizable, and is output as valid mathematical expression information; when the constant term coefficient of the denominator polynomial mathematical expression information is zero, the filter coefficient parameter information is adjusted by dividing all coefficients in the filter denominator polynomial coefficient sequence information by the constant term coefficient, so that the constant term coefficient of the new denominator polynomial mathematical expression information is normalized to one, and the coefficients of the numerator polynomial mathematical expression information are adjusted accordingly to generate the adjusted difference equation mathematical expression information of the reconfigurable digital filter.

[0080] Since the denominator coefficients have been normalized in step S125, d'(0)=1, it is directly determined to be causal and realizable, and the mathematical expression of the difference equation is output. If an abnormal situation occurs that causes the first term coefficient of the denominator to be non-1, it is corrected by normalization to ensure the causality and realizability of the system and to ensure that the filter can work as expected.

[0081] Step S1318: Perform a preliminary stability assessment on the mathematical expression of the difference equation of the reconfigurable digital filter, and calculate whether all roots of the adjusted denominator polynomial mathematical expression are inside the unit circle.

[0082] By solving for the roots of the denominator polynomial D(z)=0, the magnitudes |z_i| of the roots are obtained. If all |z_i| < 1, the filter is considered stable; otherwise, it is unstable. The polynomial roots are solved using the splitting factor method, and the calculated magnitudes are compared with 1. The stability flag is recorded as Stable = 1 (stable) or 0 (unstable). Stability is a fundamental requirement for the normal operation of a filter; an unstable filter will cause the output signal to diverge, making effective signal processing impossible.

[0083] Step S1319: When the initial stability judgment operation passes, output the mathematical expression of the difference equation of the reconfigurable digital filter to the subsequent computation flow graph instantiation step; when the initial stability judgment operation fails, feed back the unstable flag to the reconfigurable filter neural network, triggering the reconfigurable filter neural network to regenerate the filter coefficient parameter information.

[0084] If Stable=1, continue to step S132; if Stable=0, feed back a "stability failed" signal to the neural network. The neural network then regenerates the coefficient parameter information by adjusting the output layer bias of the coefficient generation branch and returns to step S131. The stability feedback mechanism ensures that the generated filter has stable characteristics, avoids divergence problems, and improves the reliability of the filter design.

[0085] Step S132: Based on the connection graph information between basic filter units and the feedback path location information in the filter topology connection relationship information in the filter structure description, instantiate the mathematical expression information of the difference equation into executable computation flow graph information.

[0086] Based on the node type list and adjacency matrix A in the topological connection information G, corresponding computational nodes are created in the simulation environment. Node types include adders, multipliers, and delay units. The nodes are connected according to the connection relationships specified in the adjacency matrix. The numerator coefficients are assigned to the multipliers in the input branch, and the denominator coefficients are assigned to the multipliers in the feedback branch. The delay order of the delay unit is set according to the order of the difference equation. The final computational flow graph contains the complete path of the signal from input to output and supports computation in discrete time steps. Computational flow graph instantiation transforms mathematical equations into executable computational models, providing an intuitive and operable platform for simulation verification.

[0087] Step S133: Set the unit impulse function as the input excitation information for the executable computational flow graph information, and initialize the internal state of all delay cells in the executable computational flow graph information to zero state information.

[0088] The unit impulse function is defined as x(n) = 1 when n = 0, and x(n) = 0 when n ≠ 0. This signal is connected to the input node of the computational flow graph, and all delay unit register values ​​are initialized to 0 to ensure the simulation starts from a zero state. The zero-state response accurately reflects the inherent characteristics of the filter, avoids the influence of the initial state on the simulation results, and makes the simulation results more valuable.

[0089] Step S134: Perform iterative calculation operations on the executable computational flow graph information in discrete-time recursive order. Calculate the signal values ​​of all nodes in the executable computational flow graph information at each discrete time point, update the internal state of the delay unit, and record the output sequence of the executable computational flow graph information under the excitation of the unit impulse function as the actual time-domain impulse response information.

[0090] Starting from n=0, the simulation is iteratively calculated in the order of n=0, 1, 2, ..., Nsim, where Nsim is the number of simulation points, set to a preset number. At each time step n, y(n) is calculated according to the difference equation, and the current y(n) is stored in the delay unit for calculation in the next time step. The output values ​​y(0), y(1), ..., y(Nsim-1) of all time steps are recorded to constitute the actual time-domain impulse response information h(n). Time-domain simulation can directly obtain the time-domain characteristics of the filter and is an important means of analyzing the transient response of the filter. The frequency characteristics of the filter can be further analyzed through the impulse response.

[0091] Step S135: Perform a discrete-time Fourier transform operation on the recorded actual time-domain impulse response information to convert the actual time-domain impulse response information to the frequency domain, thereby obtaining the actual frequency response information of the reconfigurable digital filter. The actual frequency response information includes actual amplitude response curve information and actual phase response curve information.

[0092] The Fast Fourier Transform (FFT) algorithm is used to transform h(n) to obtain the frequency response H(k) = FFT(h(n)), k = 0, 1, ..., Nsim-1. The actual amplitude response curve is |H(k)|, obtained through modulo operation; the actual phase response curve is angle(H(k)), obtained by calculating the argument of the complex number, and the result is normalized to the interval [-π, π]. The Fourier Transform converts the time-domain response into the frequency-domain response, which facilitates the analysis of the filter's frequency characteristics and understanding the filter's processing effect on signals of different frequencies.

[0093] Step S136: Extract key frequency response features from the actual frequency response information. The key frequency response features include passband cutoff frequency information, stopband start frequency information, maximum ripple amplitude information in the passband, and minimum attenuation information in the stopband, forming actual frequency domain response feature information.

[0094] The passband cutoff frequency is defined as the frequency at which the amplitude response drops to -3dB, found by linear interpolation within the passband region, corresponding to |H(k)|=10^(-3 / 20). The stopband start frequency is defined as the frequency at which the amplitude response drops to -Rs dB, where Rs is the stopband attenuation set in step S111. The maximum ripple amplitude in the passband is the difference (dB) between the maximum value of |H(k)| and 1 in the passband. The minimum attenuation in the stopband is the minimum value (dB) of |H(k)| in the stopband. These characteristic values ​​constitute the actual frequency domain response characteristic information F_act=[Fp_act, Fs_act, Rp_act, Rs_act]. Key frequency characteristics can quantify the frequency domain performance of the filter and are important indicators for evaluating whether the filter meets the design requirements. By comparing with the target characteristics, the quality of the filter design can be judged.

[0095] Step S137: Extract key time-domain response features from the actual time-domain impulse response information. The key time-domain response features include the information on the time when the impulse response peak occurs, the information on the time required for the impulse response energy to decay to a specified ratio, and the information on the number of zero-crossing points of the impulse response, to form actual time-domain response feature information.

[0096] The peak time of the impulse response is the value of n when h(n) reaches its maximum value; the time required for the energy to decay to 50% is calculated by taking the value of n when the accumulated energy sum_{i=0}^nh(i)^2 reaches 50% of the total energy sum_{i=0}^{Nsim-1}h(i)^2; the number of zero crossings is obtained by counting the number of times h(n) crosses from positive to negative or from negative to positive. These characteristic values ​​constitute the actual time-domain response characteristic information T_act=[Tp_act, Td_act, Z_act]. Key time-domain characteristics can reflect the transient response characteristics of the filter, which is of great significance for applications sensitive to time-domain characteristics, such as speech signal processing, and can help evaluate the degree of signal distortion caused by the filter.

[0097] Step S138: Merge the actual frequency response information, actual frequency domain response characteristic information, and actual time domain response characteristic information to form the actual filter response description of the reconfigurable digital filter under the current filter structure description.

[0098] The actual filter response description R_act comprises three parts: 1) actual frequency response information, including the amplitude response array |H(k)| and the phase response array angle(H(k)); 2) actual frequency domain response characteristic information F_act; and 3) actual time domain response characteristic information T_act. Organizing this information into structured data facilitates subsequent error calculation. The combined actual response description comprehensively reflects the filter's performance, enabling error assessment from multiple dimensions.

[0099] Step S139: Perform response data format normalization on the actual filter response description and output the actual filter response description after response data format normalization.

[0100] The lengths of the amplitude response array and phase response array are standardized to M points, the same as the desired frequency response sampling sequence, achieved through interpolation or truncation. Frequency and time domain characteristics are converted to the same dimensions as the corresponding parameters in the target filter response description; for example, attenuation is converted to dB, and time is converted to the number of sampling periods. The standardized actual filter response description R_act' has the same data structure and dimensions as the target filter response description Vd. This format standardization ensures the comparability between the target and actual responses, making the error assessment results more accurate and reliable.

[0101] Step S140: Compare the target filter response description with the actual filter response description to generate a filter response error description, which includes frequency domain response error information and time domain response error information.

[0102] By calculating the differences between the target and actual responses in various metrics in the frequency and time domains, the deviation of filter performance is quantified. Error calculation covers multiple dimensions such as amplitude, phase, and time-domain characteristics, ensuring a comprehensive evaluation of filter performance. This allows the optimization process to selectively adjust neural network parameters, improving the accuracy of filter design.

[0103] Step S141: Perform a point-by-point difference calculation operation in the frequency domain between the expected frequency response curve information in the target filter response description and the actual frequency response information in the actual filter response description. Calculate the absolute difference between the expected amplitude value and the actual amplitude value at each discrete frequency point to form amplitude error spectrum information.

[0104] The desired amplitude response A_des(k), k=0,1,…,M-1, is extracted from the target filter response description; the actual amplitude response A_act(k) is extracted from the actual filter response description. The amplitude error spectrum E_amp(k)=|A_des(k)-A_act(k)| is calculated to obtain the error sequence at point M, reflecting the amplitude deviation at each frequency point. The amplitude error spectrum visually demonstrates the degree of deviation of the filter's amplitude performance at each frequency point and is an important basis for analyzing the filter's frequency domain performance.

[0105] Step S142: Perform frequency domain phase difference calculation on the expected frequency response curve information in the target filter response description and the actual frequency response information in the actual filter response description. Calculate the phase difference between the expected phase value and the actual phase value at each discrete frequency point, and normalize it to a specified circumference range to form phase error spectrum information.

[0106] Extract the desired phase response φ_des(k) and the actual phase response φ_act(k), and calculate the phase difference Δφ(k) = φ_des(k) - φ_act(k). Use modulo 2π arithmetic to normalize Δφ(k) to the [-π, π] interval, obtaining the phase error spectrum E_phase(k) = Δφ(k), which is also an M-point sequence. The phase error spectrum reflects the degree of deviation of the filter's phase characteristics, and is particularly important for applications requiring linear phase; excessive phase error can lead to signal distortion.

[0107] Step S143: Perform a band weighted integration operation on the amplitude error spectrum information. Based on the importance of different frequency bands in the target filter response description, assign different error weight coefficients to the passband, transition band, and stopband, and calculate the weighted amplitude error energy value information.

[0108] The passband cutoff frequency Fp and stopband start frequency Fs are analyzed from the target filter response description, dividing the frequency band into three bands: passband (0~Fp), transition band (Fp~Fs), and stopband (Fs~Fs / 2). Weights Wp for the passband, Wt for the transition band, and Ws for the stopband are assigned, with the weight values ​​reflecting the importance of each band.

[0109] Step S1431: Extract the passband cutoff frequency information and stopband start frequency information from the target filter response description, and determine the passband frequency range, transition band frequency range and stopband frequency range based on the passband cutoff frequency information and stopband start frequency information.

[0110] The passband frequency range is [0, Fp], the transition band frequency range is [Fp, Fs], and the stopband frequency range is [Fs, Fs / 2], where Fs / 2 is the Nyquist frequency. Frequency band division is the basis for weighted error calculation, ensuring that errors in different frequency bands are weighted according to their importance, making error assessment more consistent with practical application needs.

[0111] Step S1432: Assign a passband error weighting coefficient to the passband frequency range, the passband error weighting coefficient reflecting the importance of the amplitude error in the passband to the overall performance of the filter; assign a transition band error weighting coefficient to the transition band frequency range, the transition band error weighting coefficient reflecting the importance of the amplitude error in the transition band to the overall performance of the filter; assign a stopband error weighting coefficient to the stopband frequency range, the stopband error weighting coefficient reflecting the importance of the amplitude error in the stopband to the overall performance of the filter.

[0112] The passband error weight coefficient \(W_p\) is set to a relatively large value because the amplitude fluctuation within the passband directly affects the signal transmission quality; the transition band weight \(W_t\) is the second, and the stopband weight \(W_s\) is the smallest. The specific weight values are determined according to the application scenario. For example, in speech processing, the passband weight can be set to 10, the transition band to 5, and the stopband to 1. A reasonable weight allocation can highlight the errors in important frequency bands, making the error evaluation result more meaningful in practice.

[0113] Step S1433: At all discrete frequency points within the passband frequency range, multiply the corresponding amplitude error values in the amplitude error spectrum information by the passband error weight coefficient to obtain the passband weighted amplitude error sequence information; at all discrete frequency points within the transition band frequency range, multiply the corresponding amplitude error values in the amplitude error spectrum information by the transition band error weight coefficient to obtain the transition band weighted amplitude error sequence information; at all discrete frequency points within the stopband frequency range, multiply the corresponding amplitude error values in the amplitude error spectrum information by the stopband error weight coefficient to obtain the stopband weighted amplitude error sequence information.

[0114] Traverse all frequency points \(k\) and determine the frequency band it belongs to: If \(f_k\leq F_p\), then \(E_{amp\_w}(k)=E_{amp}(k)\times W_p\); if \(F_p < f_k\leq F_s\), then \(E_{amp\_w}(k)=E_{amp}(k)\times W_t\); if \(f_k > F_s\), then \(E_{amp\_w}(k)=E_{amp}(k)\times W_s\). The weighting operation can highlight the errors in important frequency bands, making the error evaluation more in line with the actual application requirements and facilitating the subsequent optimization of neural network parameters.

[0115] Step S1434: Perform a sum of squares operation on all the values in the passband weighted amplitude error sequence information to calculate the passband weighted amplitude error energy value information; perform a sum of squares operation on all the values in the transition band weighted amplitude error sequence information to calculate the transition band weighted amplitude error energy value information; perform a sum of squares operation on all the values in the stopband weighted amplitude error sequence information to calculate the stopband weighted amplitude error energy value information.

[0116] The passband error energy \(E_p=\sum_{k\in passband}(E_{amp\_w}(k)^2)\), the transition band error energy \(E_t=\sum_{k\in transition\_band}(E_{amp\_w}(k)^2)\), and the stopband error energy \(E_s=\sum_{k\in stopband}(E_{amp\_w}(k)^2)\). The sum of squares operation converts the error sequence into an energy value, facilitating the quantification of the overall error and enabling the comparison and synthesis of errors in different frequency bands.

[0117] Step S1435: Add the passband weighted amplitude error energy value information, the transition band weighted amplitude error energy value information, and the stopband weighted amplitude error energy value information to obtain the total weighted amplitude error energy value information over the entire frequency band, which is used as the weighted amplitude error energy value information.

[0118] The total weighted amplitude error energy E_amp_total = Ep + Et + Es. The total energy value comprehensively reflects the degree of deviation of the filter's amplitude performance across all frequency bands and is an indicator for evaluating amplitude characteristics.

[0119] Step S144: Perform a linear phase deviation evaluation operation on the phase error spectrum information, and calculate the group delay change information of the phase error spectrum information in the passband frequency band. The group delay change information reflects the phase linearity error.

[0120] Group delay is defined as τ(k) = -dφ(k) / dk, obtained by numerically differentiating the phase response φ_act(k). The maximum and minimum group delay values ​​τ_max and τ_min are calculated within the passband. The change in group delay, Δτ = τ_max - τ_min, serves as a measure of phase linearity error. A smaller change in group delay indicates better phase linearity and less signal distortion, which is crucial for applications requiring high-fidelity transmission.

[0121] Step S145: Perform a time-domain feature comparison operation between the time-domain response constraint information in the target filter response description and the actual time-domain response feature information in the actual filter response description, compare the degree of satisfaction of the impulse response energy decay rate information and the group delay fluctuation constraint information, and generate time-domain constraint deviation information.

[0122] In the time-domain response constraint information, the target decay time is Td, the actual decay time is Td_act, and the decay time deviation ΔTd = |Td - Td_act|; the target group delay ripple is Tg, the actual group delay ripple is Δτ, and the group delay ripple deviation ΔTg = |Tg - Δτ|. The time-domain constraint deviation information T_err = [ΔTd, ΔTg]. The time-domain deviation information reflects the degree of deviation between the filter's time-domain characteristics and the design target, and is an important basis for evaluating the filter's time-domain performance.

[0123] Step S146: Perform error value normalization on the amplitude error spectrum information, phase error spectrum information, weighted amplitude error energy value information, group delay change information, and time-domain constraint deviation information, mapping them to a unified, dimensionless error evaluation scale to generate normalized amplitude error evaluation values, normalized phase error evaluation values, and normalized time-domain constraint deviation evaluation values; assign predetermined combined weight coefficients according to the priority of different performance indicators in the filter design objectives; based on the combined weight coefficients, perform a weighted summation operation on the normalized amplitude error evaluation values, normalized phase error evaluation values, and normalized time-domain constraint deviation evaluation values ​​to generate a scalar form of overall filter response error value information.

[0124] Normalizing E_amp_total to the [0, 1] interval yields the normalized amplitude error E_amp_norm = E_amp_total / E_amp_max, where E_amp_max is the preset maximum possible amplitude error energy. Normalizing the group delay variation Δτ yields E_phase_norm = Δτ / τ_max, where τ_max is the preset maximum allowable group delay fluctuation. The average of each element of the time-domain constraint deviation T_err after normalization yields E_time_norm = (ΔTd / Td_max + ΔTg / Tg_max) / 2. Assigning combined weights: amplitude error weight Wa, phase error weight Wp, and time-domain error weight Wt, the total error E_total = Wa * E_amp_norm + Wp * E_phase_norm + Wt * E_time_norm. The total error integrates multi-dimensional error information into a single scalar, facilitating neural network optimization and enabling the network to adjust parameters in a direction that reduces the total error.

[0125] Step S147: Encapsulate the multidimensional error vector information and the overall filter response error value information to form a complete filter response error description.

[0126] The multidimensional error vector information includes E_amp(k), E_phase(k), and T_err, with the total error being E_total. This information is combined into an error description structure. The complete error description provides comprehensive feedback information for neural network parameter optimization, including both the total error for the optimization objective and the multidimensional error to guide parameter adjustment, making the optimization process more efficient and accurate.

[0127] Step S150: Based on the filter response error description, perform adaptive adjustment and optimization operations on the internal parameters of the reconfigurable filter neural network, update the network weight parameters of the reconfigurable filter neural network, so that the filter response error description between the actual filter response description corresponding to the filter structure description output by the reconfigurable filter neural network and the target filter response description meets the preset convergence criterion.

[0128] Using the total error E_total as the optimization objective, the weight parameters of the neural network are adjusted through backpropagation to reduce the error until the convergence condition is met. The optimization process employs gradient descent combined with momentum and learning rate adaptive strategies to ensure convergence speed and stability, enabling the neural network to continuously optimize the filter structure and improve filter performance.

[0129] Step S151: Use the overall filter response error value generated after normalization and weighted fusion in the filter response error description as the loss function value, and calculate the gradient vector information of the loss function value relative to all trainable network weight parameters in the reconstructable filter neural network.

[0130] Using the total error E_total as the loss function L=E_total, the partial derivatives of L with respect to all weight parameters W in the network are calculated using the backpropagation algorithm, yielding the gradient vector ∇WL, with the dimension matching the total number of network weight parameters. Gradient calculation starts from the output layer and propagates forward layer by layer, using the chain rule to calculate the gradient of each layer's weights. The gradient vector reflects the degree of influence of each weight parameter on the loss function and serves as the basis for parameter updates; accurate gradient calculation is crucial for optimizing neural networks.

[0131] Step S152: Using a momentum-based gradient descent optimization algorithm, update the network weight parameters of the residual transformation layer of the deep feature transformation module in the reconfigurable filter neural network according to the gradient vector information, and adjust the transformation direction of the nonlinear feature transformation operation.

[0132] Momentum-based gradient descent algorithms can accelerate convergence and suppress oscillations. By accumulating historical gradient information, they can adjust the current update direction, thereby improving optimization efficiency and stability.

[0133] For example, step S1521: Obtain the current network weight parameter information of the residual transform layer of the deep feature transform module from the parameter storage of the reconfigurable filter neural network. The current network weight parameter information includes weight matrix information and bias vector information.

[0134] The weight matrix W_res and bias vector b_res of the residual transform layer are read from the network parameter cache. The dimensions of W_res are [number of input channels, number of output channels, kernel height, kernel width], and the dimension of b_res is [number of output channels]. These parameters are the key to the feature transformation of the neural network and determine the feature extraction capability. Their values ​​directly affect the performance of the network.

[0135] Step S1522: Obtain the momentum vector information corresponding to the network weight parameters of the residual transformation layer during the last iteration update from the state storage of the optimization algorithm. The dimension of the momentum vector information is the same as the dimension of the gradient vector information.

[0136] The momentum vector v_res has the same dimensions as W_res and b_res, is initialized to 0, and is stored in the optimizer's state variables. The momentum vector accumulates historical gradient information, which helps the algorithm escape local optima and accelerates convergence.

[0137] Step S1523: Multiply the gradient vector information with a preset momentum coefficient to obtain the momentum-weighted part of the gradient vector information; multiply the momentum vector information with the momentum coefficient to obtain the decay part of the momentum vector information.

[0138] The momentum coefficient γ is set to a positive number less than 1, such as 0.9. The gradient vector is ∇W_resL, with the momentum-weighted part = γ * v_res and the gradient-weighted part = (1-γ) * ∇W_resL. This weighting method balances the influence of historical momentum and current gradient, making parameter updates smoother.

[0139] Step S1524: Calculate the sum of the momentum-weighted part of the gradient vector information and the decay part of the momentum vector information to obtain the updated momentum vector information of the current iteration step; store the updated momentum vector information of the current iteration step in the state storage of the optimization algorithm, replace the old momentum vector information, and prepare for the next iteration update.

[0140] Update the momentum vector v_res_new = γ*v_res + (1-γ)*∇W_res L, and store v_res_new in the state storage, overwriting the original v_res. The updated momentum vector contains comprehensive information about the current gradient and historical momentum, which can guide the parameters to be updated in a better direction.

[0141] Step S1525: Obtain a global learning rate parameter from the state storage of the optimization algorithm. The global learning rate parameter controls the step size of the network weight parameter update.

[0142] The global learning rate η is set to a small positive number, such as 0.001, and is stored in the optimizer's hyperparameter configuration. The learning rate determines the step size of parameter updates; too large a rate may cause oscillations, while too small a rate will result in slow convergence. Setting the learning rate appropriately is crucial to the optimization effect.

[0143] Step S1526: Multiply the update momentum vector information of the current iteration step with the global learning rate parameter information to obtain the update amount information of the network weight parameters.

[0144] The weight update amount ΔW_res = η * v_res_new, and the bias update amount Δb_res = η * v_b_res_new, where v_b_res_new is the momentum update value of the bias vector. The update amount combines the effects of momentum and learning rate, controls the magnitude of parameter adjustment, and ensures the stability and effectiveness of parameter updates.

[0145] Step S1527: Subtract the update amount of the network weight parameters from the current network weight parameter information of the residual transform layer to obtain the updated network weight parameter information of the residual transform layer. Write the updated network weight parameter information of the residual transform layer back to the parameter storage of the reconfigurable filter neural network to complete one update operation of the network weight parameters of the residual transform layer.

[0146] The updated weights W_res_new = W_res - ΔW_res, and the bias b_res_new = b_res - Δb_res. W_res_new and b_res_new are then written back to the network parameter cache. Parameter updating is a core step in neural network learning; by adjusting the weights, the loss function is reduced, and the network performance is improved.

[0147] Step S1528: Repeat the above steps to update the network weight parameters of all residual transformation layers in the deep feature transformation module of the reconfigurable filter neural network until the network weight parameters of all residual transformation layers have been updated according to their corresponding gradient vector information and momentum history.

[0148] Steps S1521 to S1527 are executed one by one for the four residual transformation layers in the deep feature transformation module to complete the parameter update of all residual layers. Layer-by-layer update ensures that the parameters of each residual layer are optimized, which together improves the feature transformation capability of the network and enables the network to better capture the mapping relationship between input features and filter structure.

[0149] Step S153: Adopt an adaptive learning rate adjustment strategy to dynamically adjust the learning rate parameter of the fully connected layer of the coefficient generation branch in the reconfigurable filter neural network based on the historical trend information of the filter response error description, thereby accelerating the convergence process of the network weight parameters.

[0150] Record the total error sequence E_total from past iterations and calculate the error change rate ΔE = E_total(i) - E_total(i-1). If ΔE < 0 and continues to decrease, the learning rate is appropriate; if ΔE > 0, the learning rate is too large, and the learning rate of the coefficient generation branch is multiplied by a factor less than 1; if ΔE < 0 but the decrease is less than a threshold, the learning rate is too small, and the learning rate is multiplied by a factor greater than 1. The adjusted learning rate takes values ​​within a preset range. The adaptive learning rate can dynamically adjust the step size according to the training progress, improving convergence speed and stability, and enabling the network to find the optimal parameters faster.

[0151] Step S154: Using gradient pruning technology, the norm of the gradient vector information of the topology decoder of the topology generation branch in the reconfigurable filter neural network is checked. When the norm of the gradient vector information exceeds a preset threshold, the gradient vector information is scaled to prevent numerical instability during the network weight parameter update process.

[0152] Calculate the L2 norm ||∇W_top|| of the gradient vector of the topology decoder, with a preset threshold θ. If ||∇W_top|| > θ, then scale the gradient vector to ∇W_top' = ∇W_top * θ / ||∇W_top||, ensuring the gradient norm does not exceed the threshold. Gradient clipping prevents gradient explosion, ensures numerical stability during training, and makes network parameter updates more reliable.

[0153] Step S155: Load the updated network weight parameters of the reconfigurable filter neural network into the reconfigurable filter neural network, replace the original network weight parameters, and complete one iteration update of the network internal parameters.

[0154] All updated weight parameters (including those for the residual transform layer, coefficient generation branch, and topology generation branch) are loaded from the cache into the neural network's computation graph, overwriting the original parameters, in preparation for the next forward propagation. After the parameters are updated, the network's feature extraction and mapping capabilities are adjusted, enabling the generation of better filter structures.

[0155] Step S156: After completing the iterative update of the network's internal parameters, the target filter response description is input again into the updated reconfigurable filter neural network, and the direct structure parameter mapping operation is re-executed to generate a new filter structure description for the reconfigurable digital filter.

[0156] Using the updated network, repeat steps S121 to S129 to generate a new filter structure description. The new structure description reflects the mapping results after the network parameters are updated, and is expected to have smaller response errors and be closer to the design goal.

[0157] Step S157: Based on the new filter structure description, re-execute the filter response simulation verification operation to calculate the new actual filter response description.

[0158] Perform steps S131 to S139 to obtain the new actual filter response description R_act_new. The simulation verification process is the same as before to ensure the consistency and comparability of the results. The effect of the parameter update is evaluated by comparing the new actual response with the target response.

[0159] Step S158: Compare the target filter response description with the new actual filter response description to generate a new filter response error description.

[0160] Perform steps S141 to S147 to obtain a new error description Err_des_new, which contains the new total error E_total_new. The new error description reflects the improvement in filter performance after the parameter update.

[0161] Step S159: Check whether the overall filter response error value in the new filter response error description is less than the preset convergence threshold, or check whether the number of iterations of the network internal parameters has reached the preset maximum number of iterations.

[0162] The convergence threshold ε is set to a small positive number, such as 0.01, and the maximum number of iterations N_max is set to a preset number, such as 100. If E_total_new < ε or the number of iterations reaches N_max, the iteration stops; otherwise, return to step S151 to continue optimization. The convergence check ensures that network training stops when the error is sufficiently small or the maximum number of iterations is reached, avoiding overtraining or undertraining and ensuring training effectiveness and efficiency.

[0163] Step S1510: When the overall filter response error value in the new filter response error description is less than the preset convergence threshold, or when the number of iterations of the network internal parameters reaches the preset maximum number of iterations, stop the adaptive adjustment and optimization operation of the network internal parameters of the reconfigurable filter neural network, and save the current network weight parameters of the reconfigurable filter neural network as the final optimization result.

[0164] The current network weight parameters are saved to a file containing the values ​​of each layer's weights and biases, as well as optimizer state information, for direct loading and use later. The final filter structure description is also output as the design result. Saving the optimization results preserves the training outcomes, facilitating subsequent applications and deployments, allowing the designed filter to be quickly put into practical use.

[0165] Based on the same inventive concept, please refer to Figure 2The diagram shows a schematic block diagram of a neural network-based reconfigurable digital filter design system 100 provided in an embodiment of this application. The neural network-based reconfigurable digital filter design system 100 may include a communication unit 110, a machine-readable storage medium 120, and a processor 130.

[0166] In this embodiment, the machine-readable storage medium 120 can also be integrated into the processor 130 and can communicate and interact with external systems through the communication unit 110. The machine-readable storage medium 120 stores machine-executable instructions for implementing the scheme of this application, and the processor 130 executes the machine-executable instructions stored in the machine-readable storage medium 120 to implement the neural network-based reconfigurable digital filter design method provided in the aforementioned method embodiments.

[0167] It should be noted that, in order to simplify the description of the present invention and thus help to understand one or more embodiments of the invention, multiple features may sometimes be grouped into one embodiment, drawing or description thereof in the foregoing description of the embodiments of the present invention.

Claims

1. A method for designing reconfigurable digital filters based on neural networks, characterized in that, The method includes: Receive a target filter response description, which includes desired frequency response curve information and time-domain response constraint information; The target filter response description is input into a pre-trained reconfigurable filter neural network. The reconfigurable filter neural network performs a direct structure parameter mapping operation on the target filter response description to generate a filter structure description of the reconfigurable digital filter corresponding to the target filter response description. The filter structure description includes filter coefficient parameter information and filter topology connection information. Based on the filter coefficient parameter information and filter topology connection information in the filter structure description, a filter response simulation verification operation is performed to calculate the actual filter response description of the reconfigurable digital filter under the current filter structure description. By comparing the target filter response description with the actual filter response description, a filter response error description is generated, which includes frequency domain response error information and time domain response error information. Based on the filter response error description, the internal parameters of the reconfigurable filter neural network are adaptively adjusted and optimized, and the network weight parameters of the reconfigurable filter neural network are updated so that the filter response error description between the actual filter response description corresponding to the filter structure description output by the reconfigurable filter neural network and the target filter response description meets the preset convergence criterion.

2. The reconfigurable digital filter design method based on neural networks according to claim 1, characterized in that, The step involves inputting the target filter response description into a pre-trained reconfigurable filter neural network, and performing a direct structure parameter mapping operation on the target filter response description through the reconfigurable filter neural network to generate a filter structure description of the reconfigurable digital filter corresponding to the target filter response description, including: A multi-resolution frequency band decomposition operation is performed on the desired frequency response curve information in the target filter response description to divide the continuous frequency response curve information into multiple frequency sub-band information with overlapping regions, and extract the sub-band amplitude spectrum envelope feature information and sub-band phase change trend feature information corresponding to each frequency sub-band information. A time-domain feature encoding operation is performed on the time-domain response constraint information in the target filter response description to convert the energy decay rate constraint information and group delay fluctuation constraint information of the time-domain impulse response into time-domain constraint feature vector information. The sub-band amplitude spectrum envelope feature information, sub-band phase change trend feature information and time domain constraint feature vector information corresponding to each frequency sub-band information are subjected to cross-domain feature fusion operation to generate the fused intermediate representation information of the filter design target; The intermediate representation information of the filter design target is input into the deep feature transformation module of the reconfigurable filter neural network. The intermediate representation information of the filter design target is subjected to nonlinear feature transformation operation through multiple cascaded residual transformation layers, and high-dimensional filter design feature information is abstracted and generated layer by layer. The high-dimensional filter design feature information is input into the coefficient generation branch of the reconfigurable filter neural network. Through fully connected layers and activation functions, the filter coefficient parameter information of the reconfigurable digital filter is directly mapped and generated. The filter coefficient parameter information includes the filter numerator polynomial coefficient sequence information and the filter denominator polynomial coefficient sequence information. The high-dimensional filter design feature information is simultaneously input into the topology generation branch of the reconfigurable filter neural network. The topology structure decoder performs topology relationship reasoning operation on the high-dimensional filter design feature information to generate filter topology connection relationship information of the reconfigurable digital filter. The filter topology connection relationship information includes connection graph information between filter basic units and feedback path position information. The filter coefficient parameter information output by the coefficient generation branch of the reconfigurable filter neural network and the filter topology connection relationship information output by the topology generation branch of the reconfigurable filter neural network are combined and encapsulated with structural parameters to generate a complete filter structure description of the reconfigurable digital filter. By utilizing the filter coefficient parameter information and filter topology connection relationship information in the filter structure description of the reconfigurable digital filter, a filter structure syntax rule check operation is performed to verify the logical matching status between the filter coefficient parameter information and the filter topology connection relationship information, and a structure validity flag is generated. When the structure validity flag indicates that the structure is valid, the filter structure description of the reconfigurable digital filter is output to the filter response simulation verification operation steps; when the structure validity flag indicates that the structure is invalid, the remapping operation of the reconfigurable filter neural network is triggered, the nonlinear feature transformation operation path of the deep feature transformation module in the reconfigurable filter neural network is adjusted, and the filter structure description of the reconfigurable digital filter is regenerated.

3. The reconfigurable digital filter design method based on neural networks according to claim 1, characterized in that, Based on the filter coefficient parameter information and filter topology connection information in the filter structure description, the filter response simulation verification operation is performed to calculate the actual filter response description of the reconfigurable digital filter under the current filter structure description, including: Based on the filter coefficient parameter information in the filter structure description, including the filter numerator polynomial coefficient sequence information and the filter denominator polynomial coefficient sequence information, construct the mathematical expression information of the difference equation of the reconfigurable digital filter. Based on the connection graph information between basic filter units and the feedback path location information in the filter topology connection relationship information in the filter structure description, the mathematical expression information of the difference equation is instantiated into executable computation flow graph information; Set the unit impulse function as the input excitation information for the executable computation flow graph information, and initialize the internal state of all delay cells in the executable computation flow graph information to zero state information; The iterative computation operation of the executable computation flow graph information is executed in discrete-time recursive order. At each discrete time point, the signal values ​​of all nodes in the executable computation flow graph information are calculated, the internal state of the delay unit is updated, and the output sequence of the executable computation flow graph information under the excitation of the unit impulse function is recorded as the actual time-domain impulse response information. A discrete-time Fourier transform operation is performed on the recorded actual time-domain impulse response information to convert the actual time-domain impulse response information to the frequency domain, thereby obtaining the actual frequency response information of the reconfigurable digital filter. The actual frequency response information includes actual amplitude response curve information and actual phase response curve information. Key frequency response features are extracted from the actual frequency response information. These key frequency response features include passband cutoff frequency information, stopband start frequency information, maximum ripple amplitude information in the passband, and minimum attenuation information in the stopband, forming actual frequency domain response feature information. Key time-domain response features are extracted from actual time-domain impulse response information. These key time-domain response features include information on the timing of the impulse response peak, the time required for the impulse response energy to decay to a specified proportion, and the number of zero-crossing points of the impulse response, forming actual time-domain response feature information. The actual frequency response information, actual frequency domain response characteristic information, and actual time domain response characteristic information are combined to form the actual filter response description of the reconfigurable digital filter under the current filter structure description. Perform response data format normalization on the actual filter response description, and output the actual filter response description after response data format normalization.

4. The reconfigurable digital filter design method based on neural networks according to claim 1, characterized in that, The comparison between the target filter response description and the actual filter response description generates a filter response error description, including: A point-by-point difference calculation operation is performed on the expected frequency response curve information in the target filter response description and the actual frequency response information in the actual filter response description. The absolute difference between the expected amplitude value and the actual amplitude value at each discrete frequency point is calculated to form amplitude error spectrum information. The frequency domain phase difference calculation operation is performed on the expected frequency response curve information in the target filter response description and the actual frequency response information in the actual filter response description. The phase difference between the expected phase value and the actual phase value at each discrete frequency point is calculated and normalized to a specified circumference range to form phase error spectrum information. A frequency band weighted integral operation is performed on the amplitude error spectrum information. Based on the importance of different frequency bands in the target filter response description, different error weight coefficients are assigned to the passband, transition band and stopband, and the weighted amplitude error energy value information is calculated. A linear phase deviation evaluation operation is performed on the phase error spectrum information to calculate the group delay variation information of the phase error spectrum information in the passband frequency band, and the group delay variation information reflects the phase linearity error. A time-domain feature comparison operation is performed between the time-domain response constraint information in the target filter response description and the actual time-domain response characteristic information in the actual filter response description. The degree of satisfaction of the impulse response energy decay rate information and the group delay fluctuation constraint information is compared to generate time-domain constraint deviation information. Error value normalization is performed on the amplitude error spectrum information, phase error spectrum information, weighted amplitude error energy value information, group delay change information, and time-domain constraint deviation information, respectively, mapping them to a unified, dimensionless error evaluation scale to generate normalized amplitude error evaluation values, normalized phase error evaluation values, and normalized time-domain constraint deviation evaluation values. Based on the priority of different performance indicators in the filter design objectives, predetermined combined weight coefficients are assigned to each. Based on these combined weight coefficients, a weighted summation operation is performed on the normalized amplitude error evaluation values, normalized phase error evaluation values, and normalized time-domain constraint deviation evaluation values ​​to generate a scalar form of overall filter response error value. The multidimensional error vector information and the overall filter response error value information are encapsulated together to form a complete description of the filter response error.

5. The reconfigurable digital filter design method based on neural networks according to claim 1, characterized in that, The step of adaptively adjusting and optimizing the internal parameters of the reconfigurable filter neural network based on the filter response error description, and updating the network weight parameters of the reconfigurable filter neural network, includes: The overall filter response error value generated after normalization and weighted fusion in the filter response error description is used as the loss function value, and the gradient vector information of the loss function value relative to all trainable network weight parameters in the reconstructable filter neural network is calculated. A momentum-based gradient descent optimization algorithm is adopted to update the network weight parameters of the residual transform layer of the deep feature transform module in the reconfigurable filter neural network according to the gradient vector information, thereby adjusting the transformation direction of the nonlinear feature transform operation. An adaptive learning rate adjustment strategy is adopted to dynamically adjust the learning rate parameter of the fully connected layer of the coefficient generation branch in the reconfigurable filter neural network based on the historical trend information of the filter response error description, thereby accelerating the convergence process of the network weight parameters. Gradient pruning technique is used to check the norm of the gradient vector information of the topology decoder in the topology generation branch of the reconfigurable filter neural network. When the norm of the gradient vector information exceeds the preset threshold, the gradient vector information is scaled to prevent numerical instability in the network weight parameter update process. The updated network weight parameters of the reconfigurable filter neural network are loaded into the reconfigurable filter neural network to replace the original network weight parameters, thus completing one iteration update of the network's internal parameters. After completing the iterative update of the network's internal parameters, the target filter response description is input again into the updated reconfigurable filter neural network, and the direct structure parameter mapping operation is re-executed to generate a new filter structure description for the reconfigurable digital filter. Based on the new filter structure description, the filter response simulation verification operation is re-executed to calculate the new actual filter response description. By comparing the target filter response description with the new actual filter response description, a new filter response error description is generated. Check whether the overall filter response error value in the new filter response error description is less than the preset convergence threshold, or check whether the number of times the network internal parameters are iterated and updated has reached the preset maximum number of iterations. When the overall filter response error value in the new filter response error description is less than the preset convergence threshold, or when the number of iterations of the network internal parameters reaches the preset maximum number of iterations, the adaptive adjustment and optimization operation of the network internal parameters of the reconfigurable filter neural network is stopped, and the current network weight parameters of the reconfigurable filter neural network are saved as the final optimization result.

6. The method for designing reconfigurable digital filters based on neural networks according to claim 1, characterized in that, The received target filter response description, which includes desired frequency response curve information and time-domain response constraint information, includes: The system receives the desired filter performance indicators input by the user through a graphical interface or configuration file. The desired filter performance indicators include passband cutoff frequency information, stopband start frequency information, maximum allowable ripple amplitude information in the passband, and minimum required attenuation information in the stopband. Based on the desired filter performance index, an interpolation algorithm is used to generate a continuous and smooth desired frequency response curve. The desired frequency response curve includes the desired amplitude value information corresponding to each frequency point in the range from zero frequency to Nyquist frequency. According to the time domain requirements of the filter design scenario, the system receives user-specified time domain response constraint information, which includes the maximum overshoot amplitude limit information of the impulse response, the time length limit information required for the impulse response energy to decay to a specified percentage, and the group delay fluctuation range limit information. The desired frequency response curve information is encrypted by frequency domain sampling points. The sampling point density is automatically increased in the frequency band region where the frequency response changes drastically, generating high-resolution desired frequency response sampling sequence information. The time-domain response constraint information is quantized using time-domain parameters, converting the non-quantized constraint information into quantized constraint vector information with a specific numerical range. The high-resolution desired frequency response sampling sequence information and quantization constraint vector information are format aligned and concatenated to form a target filter response description vector of a unified dimension. Normalize and scale the target filter response description vector to generate a normalized target filter response description. Before inputting the normalized target filter response description into the reconfigurable filter neural network, perform a description integrity verification operation to check whether the target filter response description vector contains valid data and whether there is any missing data. When the description integrity verification operation passes, the target filter response description is fed into the reconfigurable filter neural network for subsequent direct structure parameter mapping operations; when the description integrity verification operation fails, the user is prompted with a message indicating that the data is missing or invalid, and the system waits to receive a complete and valid target filter response description again.

7. The method for designing reconfigurable digital filters based on neural networks according to claim 2, characterized in that, The multi-resolution band decomposition operation on the desired frequency response curve information in the target filter response description divides the continuous frequency response curve information into multiple frequency sub-band information with overlapping regions, including: Apply a windowed Fourier transform operation to the desired frequency response curve information. Convolve the desired frequency response curve information through a set of analysis window functions with center frequencies distributed at fixed intervals and gradually increasing bandwidth to generate a set of time-frequency coefficient information with different time-frequency resolutions. Based on the amplitude distribution of the time-frequency coefficient information, identify the frequency bands with gentle amplitude changes and the transitional frequency bands with drastic amplitude changes in the desired frequency response curve information, and generate frequency band characteristic classification information. Based on frequency band characteristic classification information, a wider frequency sub-band division width is allocated to frequency bands with gentle amplitude changes, and a narrower frequency sub-band division width is allocated to transitional frequency bands with drastic amplitude changes, thereby generating adaptive frequency division scheme information. According to the adaptive frequency division scheme information, a set of frequency band boundary points with overlapping regions are defined on the frequency axis. The frequency band boundary points divide the continuous frequency response curve information into multiple frequency interval information with overlapping beginning and end parts. Within each frequency range, the amplitude value sequence of the desired frequency response curve is extracted to form the amplitude sub-band information corresponding to that frequency range; within each frequency range, the phase value sequence of the desired frequency response curve is extracted to form the phase sub-band information corresponding to that frequency range. Envelope extraction is performed on each amplitude sub-band information. High-frequency fluctuation components in the amplitude sub-band information are removed by low-pass filtering to obtain smooth amplitude sub-band envelope information, which serves as the sub-band amplitude spectrum envelope feature information. Trend analysis is performed on each phase sub-band information. The slope of the straight line that changes with frequency is fitted by linear regression. The slope of the straight line is used as the average phase change rate information of the sub-band. The residual fluctuation information of the phase sub-band information relative to the fitted straight line is calculated, which together constitute the sub-band phase change trend feature information. The sub-band amplitude spectrum envelope feature information and sub-band phase change trend feature information corresponding to each frequency interval are combined to form a complete representation of the frequency sub-band information. All complete representations of frequency sub-band information are arranged in order from low to high frequency to form the multi-resolution frequency band decomposition result of the desired frequency response curve information in the target filter response description.

8. The method for designing reconfigurable digital filters based on neural networks according to claim 3, characterized in that, The step of constructing the mathematical expression of the difference equation for a reconfigurable digital filter based on the filter coefficient parameter information in the filter structure description, including the filter numerator polynomial coefficient sequence information and the filter denominator polynomial coefficient sequence information, includes: The filter numerator polynomial coefficient sequence information is parsed from the filter coefficient parameter information. The filter numerator polynomial coefficient sequence information is a sequence containing multiple real or complex values. Each value in the sequence represents the coefficient of different delay terms of the input signal in the difference equation. The filter denominator polynomial coefficient sequence information is parsed from the filter coefficient parameter information. The filter denominator polynomial coefficient sequence information is a sequence containing multiple real or complex values. The first value in the sequence is set to one, and the subsequent values ​​represent the coefficients of different delay terms of the output signal in the difference equation. Arrange the coefficients in the filter numerator polynomial coefficient sequence information in order of delay order from low to high to form the mathematical expression information of the numerator polynomial of the difference equation of the reconfigurable digital filter. Arrange the coefficients in the filter denominator polynomial coefficient sequence information in order of delay order from low to high to form the mathematical expression information of the denominator polynomial of the difference equation of the reconfigurable digital filter. Based on the standard form of the difference equation of a digital filter, using the mathematical expression information of the numerator polynomial and the mathematical expression information of the denominator polynomial, the input-output relationship expressed in discrete time series form is written. The output of this relationship is the mathematical expression information of the difference equation of the reconfigurable digital filter. Verify whether the mathematical expression of the difference equation of the reconfigurable digital filter satisfies the causal system condition, and check whether the coefficient of the constant term in the mathematical expression of the denominator polynomial is zero; When the coefficient of the constant term in the mathematical expression of the denominator polynomial is not zero, the mathematical expression of the difference equation of the reconfigurable digital filter is considered causal and realizable, and is output as an effective mathematical expression. When the constant term coefficient of the denominator polynomial mathematical expression is zero, the filter coefficient parameter information is adjusted by dividing all coefficients in the filter denominator polynomial coefficient sequence information by the constant term coefficient, so that the constant term coefficient of the new denominator polynomial mathematical expression information is normalized to one, and the coefficients of the numerator polynomial mathematical expression information are adjusted accordingly to generate the adjusted difference equation mathematical expression information of the reconfigurable digital filter. A preliminary stability assessment is performed on the mathematical expression of the difference equation of the reconfigurable digital filter, and it is calculated whether all roots of the adjusted denominator polynomial mathematical expression are inside the unit circle. When the initial stability assessment passes, the mathematical expression of the difference equation of the reconfigurable digital filter is output to the subsequent computational flow graph instantiation step; when the initial stability assessment fails, the instability flag is fed back to the reconfigurable filter neural network, triggering the reconfigurable filter neural network to regenerate the filter coefficient parameter information.

9. The reconfigurable digital filter design method based on neural networks according to claim 4, characterized in that, The step of performing a band-weighted integration operation on the amplitude error spectrum information involves assigning different error weight coefficients to the passband, transition band, and stopband based on the importance of different frequency bands in the target filter response description, and calculating the weighted amplitude error energy value information, including: The passband cutoff frequency information and stopband start frequency information are extracted from the target filter response description. Based on the passband cutoff frequency information and stopband start frequency information, the passband frequency range, transition band frequency range and stopband frequency range are determined. A passband error weighting coefficient is assigned to the passband frequency range, which reflects the importance of the amplitude error within the passband to the overall performance of the filter; a transition band error weighting coefficient is assigned to the transition band frequency range, which reflects the importance of the amplitude error within the transition band to the overall performance of the filter; and a stopband error weighting coefficient is assigned to the stopband frequency range, which reflects the importance of the amplitude error within the stopband to the overall performance of the filter. At all discrete frequency points within the passband, the corresponding amplitude error value in the amplitude error spectrum information is multiplied by the passband error weighting coefficient to obtain the passband weighted amplitude error sequence information; at all discrete frequency points within the transition band, the corresponding amplitude error value in the amplitude error spectrum information is multiplied by the transition band error weighting coefficient to obtain the transition band weighted amplitude error sequence information; at all discrete frequency points within the stopband, the corresponding amplitude error value in the amplitude error spectrum information is multiplied by the stopband error weighting coefficient to obtain the stopband weighted amplitude error sequence information. The passband weighted amplitude error energy value is calculated by performing a sum of squares operation on all values ​​in the passband weighted amplitude error sequence information; the transition band weighted amplitude error energy value is calculated by performing a sum of squares operation on all values ​​in the transition band weighted amplitude error sequence information; and the stopband weighted amplitude error energy value is calculated by performing a sum of squares operation on all values ​​in the stopband weighted amplitude error sequence information. The passband weighted amplitude error energy value, the transition band weighted amplitude error energy value, and the stopband weighted amplitude error energy value are added together to obtain the total weighted amplitude error energy value over the entire frequency band, which is used as the weighted amplitude error energy value.

10. A design system for reconfigurable digital filters based on neural networks, characterized in that, include: processor; A machine-readable storage medium for storing machine-executable instructions of the processor; The processor is configured to execute the neural network-based reconfigurable digital filter design method according to any one of claims 1 to 9 by executing the machine-executable instructions.

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