Critical sampling circuit bandwidth extension method and system

Abstract

The invention discloses a critical sampling circuit bandwidth extension method and system, and belongs to the technical field of signal sampling. The implementation method comprises the following steps: S1, estimating a model coefficient of a critical sampling circuit analog channel amplitude square response through super-relaxation primitive dual estimation, constructing an analog channel response matrix, and combining row extraction to obtain a system response matrix; s2, establishing a critical sampling circuit high-dimensional response matrix and completing parameter initialization; s3, performing extended feature iterative solution through elastic network regression, performing convergence check on extended residual errors or iteration times, if the convergence check is satisfied, turning to S4, otherwise, continuing iteration; and S4, reconstructing a high-dimensional signal by using the extension characteristic solved in the step S3, and obtaining a reconstructed signal after bandwidth extension is performed on the critical sampling circuit through sampling rate conversion. According to the method, the spectrum characteristics in the target extension bandwidth of the critical sampling circuit are iteratively solved, out-of-band lost spectrum information can be recovered without improving the sampling clock frequency and the analog input bandwidth, and low-cost high-frequency signal sampling is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of signal sampling, and relates to a critical sampling circuit bandwidth extension method and system. Background Art

[0002] The sampling rate of the critical sampling circuit is twice the analog input bandwidth of the system. If the input signal bandwidth exceeds the system analog bandwidth, the "insufficient bandwidth" of the critical sampling circuit may cause the signal energy outside the 3dB cutoff band to be suppressed by the system frequency response transition band and stop band, resulting in the loss of high-frequency information of the signal; even if the out-of-band signal is not effectively suppressed and there is residual energy, it will be under-sampling due to the "insufficient sampling rate" of the critical sampling circuit, causing aliasing effect. The bandwidth extension problem of the critical sampling circuit refers to the undistorted recovery of high-frequency information outside the 3dB cutoff band of the critical sampling circuit through the back-end digital signal processing without changing the sampling rate of the analog-to-digital converter ADC of the critical sampling circuit. Different from the under-sampling problem of "insufficient sampling rate" or the bandwidth extension problem of "insufficient bandwidth", the characteristics of "insufficient bandwidth and insufficient sampling rate" make it seriously ill-posed and therefore more challenging. At present, there is no effective solution to this type of problem. Summary of the invention

[0003] The object of the present invention is to provide a critical sampling circuit bandwidth extension method and system, which can extend the circuit sampling bandwidth without increasing the sampling rate and realize low-cost high-frequency signal sampling.

[0004] The purpose of the present invention is achieved through the following technical solutions.

[0005] The present invention discloses a critical sampling circuit bandwidth extension method, comprising the following steps:

[0006] S1. Use a polyphonic or linear frequency modulation signal to measure the amplitude square response of the critical sampling circuit simulation channel to be extended; take the l1 norm of the difference between the amplitude square response to be estimated and the measured amplitude square response as the objective function, and introduce a super-relaxation parameter to convert the original non-convex and non-concave fractional polynomial nonlinear programming problem about the objective function into a constrained convex optimization dual problem, and use the interior point method to solve and obtain the coefficient vector of the amplitude square response to be estimated; use the coefficient vector of the amplitude square response to be estimated to construct a linear equation, and solve and obtain the frequency response of the critical sampling circuit simulation channel; construct the response matrix of the critical sampling circuit simulation channel, and perform row extraction on the response matrix of the critical sampling circuit simulation channel to obtain the system response matrix of the critical sampling circuit.

[0007] S1.1. Generate a multi-tone or linear frequency modulation signal as a test signal. The generated test signal has I frequency points evenly distributed in the frequency range (0, MB), where M is an integer greater than 1, and B = Fs / 2 is the analog input bandwidth of the critical sampling circuit, F s is the sampling rate of the ADC in the critical sampling circuit. The test signal is input into the analog channel of the critical sampling circuit, and the output of the analog channel is oversampled M times using an additional reference ADC, that is, the sampling rate of the reference ADC is MF s The measured amplitude square response of the analog channel is obtained based on the test signal and the oversampled output signal.

[0008] S1.2, take the l1 norm of the difference between the estimated amplitude square response and the measured amplitude square response as the objective function to construct the following optimization problem

[0009]

[0010] The estimated amplitude square response is modeled using an L-order autoregressive moving average model, symbol For example Corresponding to the I frequency points in S1.1,

[0011]

[0012] Where 0 L×1 represents an L-row all-zero column vector, is the coefficient vector of the L-order magnitude square response to be estimated;

[0013] S1.3. For i=0,1,…,I-1, use the interior point method or gradient descent method to solve the following 2I convex optimization problems

[0014]

[0015] S1.4. Introducing the super-relaxation parameter λ i , using l calculated by S1.3 i and i As λ i The upper and lower boundary constraints are used to transform the original non-convex and non-concave fractional polynomial nonlinear programming problem constructed in S1.2 into the following constrained super-relaxed convex optimization dual problem:

[0016]

[0017] Use the interior point method or augmented Lagrangian method to solve the coefficient vector of the magnitude square response to be estimated

[0018] S1.5. Constructing a system of linear equations

[0019]

[0020] in

[0021]

[0022] Use the least squares method to solve (5) to obtain the parameters of the frequency response to be estimated and The frequency response of the critical sampling circuit analog channel is obtained by the following formula (7):

[0023]

[0024] Perform inverse discrete Fourier transform on equation (7) to obtain the unit impulse response h[n] of the analog channel;

[0025] S1.6. Use the unit impulse response h[n] of the critical sampling circuit simulation channel to construct the response matrix of the critical sampling circuit simulation channel:

[0026]

[0027] Where K is the order of the matrix H. The response matrix H of the critical sampling circuit simulation channel K×K Perform M-fold row extraction to obtain the system response matrix of the critical sampling circuit

[0028] S2. Construct feature transformation space, combine the critical sampling circuit system response matrix constructed in S1, and establish the response matrix model of critical sampling circuit to high-dimensional input space; initialize the number of iterations, high-dimensional input space, number of extended features, unlocated extended feature index space, located extended feature index space, extended feature response matrix, and bandwidth extension residual.

[0029] S2.1. Constructing feature transformation space

[0030]

[0031] in The response matrix of the critical sampling circuit system constructed in combination with S1.3 Establishing the response matrix model of critical sampling circuit to high-dimensional input space

[0032]

[0033] where a k is the kth atom of the high-dimensional input spatial response matrix Ξ, hereinafter referred to as the high-dimensional response matrix;

[0034] S2.2, let the number of iterations j = 0, the high-dimensional input space ξ = 0 K×1, the number of extended features is S; initialize the unlocated extended feature index space K = {k|k = 0, 1, ..., K / 2 (1-1 / M), K / 2 (1+1 / M), ..., K-2, K-1}, which is composed of the index of the unlocated features in the target extended bandwidth in the high-dimensional input space; the located extended feature index space It is composed of the index of the located extended features in the target extended bandwidth in the high-dimensional input space; the extended feature response matrix Bandwidth extension residual Where y is the output signal of the critical sampling circuit.

[0035] S3. Iteratively solve the extended feature vector: in each iterative solution, update the unlocated extended feature index space by eliminating the index of the already located extended features in the target extended bandwidth in the high-dimensional input space; in the updated unlocated extended feature index space, relocate the feature atoms with the largest correlation with the bandwidth extension residual, and update the feature index space; according to the updated feature index space, update the extended feature response matrix, construct the elastic network regression objective function, and use the interior point method to solve the extended feature vector; update the bandwidth extension residual according to the extended feature vector, perform a convergence check, terminate the iteration if satisfied, and transfer the final solved extended feature vector to S4, otherwise continue the iteration.

[0036] S3.1, let the number of iterations j = j + 1, remove the index of the located extended feature in the target extended bandwidth in the high-dimensional input space from the index space of the unlocated extended feature, that is, update K = K\w;

[0037] S3.2, using the unlocated extended features corresponding to the atoms to construct the matrix Λ = {a k |k∈K}, through c=Λ T rCalculate the correlation between the atoms corresponding to the unlocated extended features and the bandwidth extension residuals, and find the atom a with the largest correlation with the bandwidth extension residuals k’ , update the located extended feature index space w[i]=k';

[0038] S3.3. Atom a found according to S3.2 k’ , update the extended feature response matrix Ξ n =[Ξ n ,a k' ], construct the following objective function based on elastic network regression

[0039]

[0040] Where η is the regularization parameter and μ∈[0,1] is the mixing parameter. The extended eigenvector is obtained by solving equation (11) using the interior point method

[0041] S3.4. Update bandwidth extension residual

[0042] S3.5, convergence check: If ||r||2 is less than the set threshold or j≥S, execute S4; otherwise, return to S3.1.

[0043] S4. Use the extended feature vector solved by S3 to update the high-dimensional input space, combine the feature transformation space to obtain a high-dimensional reconstructed signal, perform sampling rate conversion on the high-dimensional reconstructed signal, and obtain a reconstructed signal after bandwidth extension of the critical sampling circuit.

[0044] S4.1. Update the high-dimensional input space using the extended feature vector obtained in S3:

[0045]

[0046] S4.2. Use the high-dimensional input space and feature transformation space to obtain a high-dimensional reconstructed signal, that is, x'=E H ξ; Perform sampling rate conversion on the high-dimensional reconstructed signal x', and the conversion factor is MF s / 2B u , and the sampling rate is 2B u The low-dimensional reconstructed signal x is obtained. At this time, the sampling bandwidth of the critical sampling circuit is extended from the original B to B u .

[0047] The present invention also discloses a critical sampling circuit bandwidth extension system, which is used to implement the critical sampling circuit bandwidth extension method described above. The critical sampling circuit bandwidth extension system includes a system response estimation module, an extension initialization module, an extension feature iterative solution module and a broadband signal reconstruction module.

[0048] The system response estimation module is used to measure the amplitude square response of the analog channel of the critical sampling circuit to be extended, and solve the model coefficient of the amplitude square response to be estimated by minimizing the l1 norm of the difference between the amplitude square response to be estimated and the measured amplitude square response, so as to obtain the frequency response and unit impulse response of the analog channel of the critical sampling circuit; then, the response matrix of the analog channel of the critical sampling circuit is constructed, and the response matrix of the analog channel of the critical sampling circuit is row-extracted to obtain the system response matrix of the critical sampling circuit, which is used for parameter initialization of the extended initialization module.

[0049] The extended initialization module is used to initialize the parameters of the extended feature iterative solution module using the system response matrix output by the system response estimation module, and input the initialized parameters into the extended feature iterative solution module.

[0050] The extended feature iterative solution module is used to locate the extended feature most relevant to the current extended residual within the target extended bandwidth in each iteration, use the located extended features to reduce the dimension of the high-dimensional response matrix to obtain a low-dimensional extended feature response matrix, solve the extended feature vector through elastic network regression and update the extended residual, which is used for the extended feature location and residual update of the next iteration, and perform a convergence check on the extended residual or the number of iterations; if satisfied, the solved extended feature vector is input into the broadband signal reconstruction module, otherwise the iteration continues.

[0051] The broadband signal reconstruction module is used to update the high-dimensional input space using the extended feature vector output by the extended feature iterative solution module, obtain the high-dimensional reconstructed signal in combination with the feature transformation space, perform sampling rate conversion on the high-dimensional reconstructed signal, and obtain the reconstructed signal after the bandwidth of the critical sampling circuit is extended.

[0052] Beneficial effects:

[0053] 1. A critical sampling circuit bandwidth extension method and system disclosed in the present invention converts the non-convex and non-concave fractional polynomial nonlinear programming problem for critical sampling circuit analog channel frequency response parameter estimation into a constrained convex optimization problem through super-relaxed primal duality, thereby reducing the computational complexity of the critical sampling circuit analog channel frequency response parameter estimation problem and improving the efficiency of critical sampling circuit bandwidth extension.

[0054] 2. The present invention discloses a critical sampling circuit bandwidth extension method and system, which constrains the feature search range within the target extension bandwidth in the extension initialization stage, thereby suppressing the aliasing effect caused by insufficient sampling rate when the critical sampling circuit samples the high-frequency components of the signal, and improving the reconstruction accuracy of the bandwidth extension signal.

[0055] 3. The present invention discloses a critical sampling circuit bandwidth extension method and system, which can solve the serious ill-posed problem of extended feature solution caused by insufficient bandwidth and loss of high-frequency signal information of the critical sampling circuit by reducing the dimensionality of the high-dimensional response matrix of the critical sampling circuit, thereby improving the accuracy and efficiency of the critical sampling circuit bandwidth extension.

[0056] 4. The present invention discloses a critical sampling circuit bandwidth extension method and system, which adopts the critical sampling circuit bandwidth extension method to perform signal sampling without increasing the sampling clock frequency and the analog input bandwidth, and can restore the spectrum information lost out of the band, thereby realizing low-cost high-frequency signal sampling. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0058] Figure 1 The flowchart of the critical sampling circuit bandwidth extension method is as follows;

[0059] Figure 2 The time-frequency domain waveforms of a 64QAM multi-carrier signal before and after bandwidth extension in the embodiment, wherein the number of carriers of the multi-carrier signal is 2, and the sub-carrier center frequencies are located at 100 MHz and 230 MHz respectively;

[0060] Figure 3 is the residual convergence performance corresponding to different η and μ in the embodiment. DETAILED DESCRIPTION

[0061] The present invention is further described and described in detail below with reference to the accompanying drawings and embodiments.

[0062] like Figure 1 As shown, the present embodiment discloses a critical sampling circuit bandwidth extension method, and the specific implementation steps are as follows:

[0063] S1. System response estimation, as follows:

[0064] S1.1. Generate a multi-tone signal of I=600 as a test signal, with its frequency points evenly distributed within (0,1GHz). Input the test signal into the analog channel of the critical sampling circuit, the critical sampling circuit sampling rate is 400MSPS, and the analog input bandwidth is 200MHz; use the reference ADC with a sampling rate of 2GSPS to oversample the output of the analog channel by 5 times. According to the test signal and the oversampled output signal, the measured amplitude square response of the analog channel is obtained.

[0065] S1.2, take the l1 norm of the difference between the estimated amplitude square response and the measured amplitude square response as the objective function to construct the following optimization problem

[0066]

[0067] The estimated magnitude squared response is modeled using an L=15 order autoregressive moving average model.

[0068] S1.3. Use gradient descent to solve the following convex optimization problem

[0069]

[0070] S1.4. Introducing the super-relaxation parameter λ i , using l calculated by S1.3 i and i As λ i The upper and lower boundary constraints are used to transform the non-convex and non-concave fractional polynomial nonlinear programming problem constructed in S1.2 into the following constrained convex optimization problem:

[0071]

[0072] λ i ∈(l i ,υ i )

[0073] The coefficient vector of the magnitude square response to be estimated is obtained by using the augmented Lagrangian method

[0074] S1.5. Constructing a system of linear equations

[0075]

[0076] in

[0077]

[0078] Use the least squares method to obtain the parameters of the frequency response to be estimated and The frequency response of the critical sampling circuit analog channel is obtained by the following formula

[0079]

[0080] Perform inverse discrete Fourier transform to obtain the unit impulse response h[n] of the analog channel;

[0081] S1.6. Use the unit impulse response h[n] of the critical sampling circuit simulation channel to construct the response matrix of the critical sampling circuit simulation channel:

[0082]

[0083] The order K of H is 4000. The response matrix H of the critical sampling circuit simulation channel 4000×4000 Perform 5-fold row decimation to obtain the system response matrix of the critical sampling circuit

[0084] S2, extended initialization, as follows:

[0085] S2.1. Constructing feature transformation space

[0086]

[0087] The response matrix of the critical sampling circuit system constructed in combination with S1.3 Establishing a high-dimensional response matrix for critical sampling circuits

[0088]

[0089] S2.2, let the number of iterations j = 0, ξ = 0 4000×1 , S = 200; initialize K = {k|k = 0, 1, ..., 1600, 2400, ..., 3998, 3999};

[0090] S3, extended feature iterative solution, as follows:

[0091] S3.1, let the number of iterations j = j + 1, remove the index of the located extended features in the target extended bandwidth in the high-dimensional input space from the index space of the unlocated extended features, that is, update K = K\w;

[0092] S3.2, using the unlocated extended features corresponding to the atoms to construct the matrix Λ = {a k |k∈K}, through c=Λ T r Calculate the correlation between the atoms corresponding to the unlocated extended features and the bandwidth extension residuals, and find the atom a with the largest correlation with the bandwidth extension residuals k’ , update the located extended feature index space w[i]=k';

[0093] S3.3. Update the extended feature response matrix Ξ n =[Ξ n ,a k' ], construct the following objective function based on elastic network regression

[0094]

[0095] Where η is the regularization parameter and μ∈[0,1] is the mixing parameter. The extended eigenvector is obtained by solving equation (11) using the interior point method

[0096] S3.4. Update bandwidth extension residual

[0097] S3.5, convergence check: If ||r||2 is less than the set threshold or j≥S, execute S4; otherwise, return to S3.1.

[0098] S4, broadband signal reconstruction, as follows:

[0099] S4.1. Update the high-dimensional input space using the extended feature vector obtained in S3:

[0100]

[0101] S4.2. Use the high-dimensional input space and feature transformation space to obtain a high-dimensional reconstructed signal, that is, x'=E H ξ; The high-dimensional reconstructed signal x' is downsampled by 4 times to obtain a low-dimensional reconstructed signal x with a sampling rate of 500MSPS. At this time, the sampling bandwidth of the critical sampling circuit is extended from the original 200MHz to 250MHz.

[0102] The critical sampling circuit sampling rate of this embodiment is 400MSPS, and the analog input bandwidth is 200MHz. x(t) is a 64QAM multi-carrier signal, the number of carriers is 2, and the subcarrier center frequencies are located at 100MHz and 230MHz respectively; the bandwidth extension target is 250MHz, and the sampling rate of the signal after extension is 500MSPS. The time domain waveform comparison before and after bandwidth extension is as follows: Figure 2 As shown, Figure 3 The residual convergence performance corresponding to different η and μ in the embodiment is demonstrated.

[0103] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A critical sampling circuit bandwidth extension method, characterized in that: The following steps are included: S1. Measuring the amplitude square response of the analog channel of the critical sampling circuit to be extended using a multi-tone or linear frequency modulation signal; Taking the l1 norm of the difference between the estimated amplitude square response and the measured amplitude square response as the objective function, the non-convex and non-concave fractional polynomial nonlinear programming original problem about the objective function is converted into a constrained convex optimization dual problem by introducing a super-relaxation parameter, and the coefficient vector of the estimated amplitude square response is obtained by using the interior point method; a linear equation is constructed using the coefficient vector of the estimated amplitude square response, and the frequency response of the critical sampling circuit simulation channel is obtained by solving it; a response matrix of the critical sampling circuit simulation channel is constructed, and the response matrix of the critical sampling circuit simulation channel is row-decimated to obtain the system response matrix of the critical sampling circuit; S2, construct feature transformation space, combine the critical sampling circuit system response matrix constructed in S1, and establish the response matrix model of the critical sampling circuit to the high-dimensional input space; initialize the number of iterations, high-dimensional input space, number of extended features, unlocated extended feature index space, located extended feature index space, extended feature response matrix, and bandwidth extension residual; S3, iteratively solving the extended feature vector: in each iterative solution, the index space of the unlocated extended feature is updated by eliminating the index of the located extended feature in the high-dimensional input space within the target extended bandwidth; In the updated unlocated extended feature index space, relocate the feature atom with the largest correlation with the bandwidth extended residual, and update the feature index space; According to the updated feature index space, the extended feature response matrix is ​​updated, the elastic network regression objective function is constructed, and the extended feature vector is solved using the interior point method; the bandwidth extended residual is updated according to the extended feature vector, and a convergence check is performed. If the convergence is satisfied, the iteration is terminated and the final solved extended feature vector is transferred to S4, otherwise the iteration continues; S4. Use the extended feature vector solved by S3 to update the high-dimensional input space, combine the feature transformation space to obtain a high-dimensional reconstructed signal, perform sampling rate conversion on the high-dimensional reconstructed signal, and obtain a reconstructed signal after bandwidth extension of the critical sampling circuit.

2. A critical sampling circuit bandwidth extension method as claimed in claim 1, characterized in that: The implementation method of step S1 is: S1.

1. Generate a multi-tone or linear frequency modulation signal as a test signal. The generated test signal has I frequency points evenly distributed in the frequency range (0, MB), where M is an integer greater than 1, and B = F s / 2 is the analog input bandwidth of the critical sampling circuit, F s is the sampling rate of the ADC in the critical sampling circuit; the test signal is input into the analog channel of the critical sampling circuit, and the output of the analog channel is oversampled M times by using an additional reference ADC, that is, the sampling rate of the reference ADC is MF s ;According to the test signal and the oversampled output signal, the measured amplitude square response of the analog channel is obtained i=0,1,...,I-1; S1.2, take the l1 norm of the difference between the estimated amplitude square response and the measured amplitude square response as the objective function to construct the following optimization problem The estimated amplitude square response is modeled using an L-order autoregressive moving average model, symbol For example Corresponding to the I frequency points in S1.1, Where 0 L×1 represents an L-row all-zero column vector, is the coefficient vector of the L-order magnitude square response to be estimated; S1.

3. For i=0,1,…,I-1, use the interior point method or gradient descent method to solve the following 2I convex optimization problems S1.

4. Introducing the super-relaxation parameter λ i , calculated using S1.3 and i As λ i The upper and lower boundary constraints are used to transform the original non-convex and non-concave fractional polynomial nonlinear programming problem constructed in S1.2 into the following constrained super-relaxed convex optimization dual problem: Use the interior point method or augmented Lagrangian method to solve the coefficient vector of the magnitude square response to be estimated S1.

5. Constructing a system of linear equations in Use the least squares method to solve (5) to obtain the parameters of the frequency response to be estimated and The frequency response of the critical sampling circuit analog channel is obtained by the following formula (7): Perform inverse discrete Fourier transform on equation (7) to obtain the unit impulse response h[n] of the analog channel; S1.

6. Use the unit impulse response h[n] of the critical sampling circuit simulation channel to construct the response matrix of the critical sampling circuit simulation channel: Where K is the order of the matrix H; the response matrix H of the critical sampling circuit simulation channel K×K Perform M-fold row extraction to obtain the system response matrix of the critical sampling circuit 3. A critical sampling circuit bandwidth extension method as claimed in claim 2, characterized in that: The implementation method of step S2 is: S2.

1. Constructing feature transformation space in The response matrix of the critical sampling circuit system constructed in combination with S1.3 Establishing the response matrix model of critical sampling circuit to high-dimensional input space where a k is the kth atom of the high-dimensional input spatial response matrix Ξ, hereinafter referred to as the high-dimensional response matrix; S2.2, let the number of iterations j = 0, the high-dimensional input space ξ = 0 K×1 , the number of extended features is S; initialize the unlocated extended feature index space K = {k|k = 0, 1, ..., K / 2 (1-1 / M), K / 2 (1+1 / M), ..., K-2, K-1}, which is composed of the index of the unlocated features in the target extended bandwidth in the high-dimensional input space; the located extended feature index space It is composed of the index of the located extended features within the target extended bandwidth in the high-dimensional input space; Extended Characteristic Response Matrix Bandwidth extension residual Where y is the output signal of the critical sampling circuit.

4. A critical sampling circuit bandwidth extension method as claimed in claim 3, characterized in that: The implementation method of step S3 is: S3.1, let the number of iterations j = j + 1, remove the index of the located extended features in the target extended bandwidth in the high-dimensional input space from the index space of the unlocated extended features, that is, update K = K\w; S3.2, using the unlocated extended features corresponding to the atoms to construct the matrix Λ = {a k |k∈K}, through c=Λ T r Calculate the correlation between the atoms corresponding to the unlocated extended features and the bandwidth extension residuals, and find the atom a with the largest correlation with the bandwidth extension residuals k’ , update the located extended feature index space w[i]=k'; S3.

3. Atom a found according to S3.2 k’ , update the extended feature response matrix Ξ n =[Ξ n ,a k' ], construct the following objective function based on elastic network regression Where η is the regularization parameter and μ∈[0,1] is the mixing parameter. The extended eigenvector is obtained by solving equation (11) using the interior point method. S3.

4. Update bandwidth extension residual S3.5, convergence check: If ||r||2 is less than the set threshold or j≥S, execute S4; otherwise, return to S3.

1.

5. A critical sampling circuit bandwidth extension method as claimed in claim 4, characterized in that: The implementation method of step S4 is: S4.

1. Update the high-dimensional input space using the extended feature vector obtained in S3: S4.

2. Use the high-dimensional input space and feature transformation space to obtain a high-dimensional reconstructed signal, that is, x'=E H ξ; Perform sampling rate conversion on the high-dimensional reconstructed signal x', and the conversion factor is MF s / 2B u , the sampling rate is 2B u The low-dimensional reconstructed signal x is obtained. At this time, the sampling bandwidth of the critical sampling circuit is extended from the original B to B u .

6. A critical sampling circuit bandwidth extension system, used to implement a critical sampling circuit bandwidth extension method as claimed in claim 1, 2, 3, 4 or 5, characterized in that: It includes a system response estimation module, an extension initialization module, an extension feature iterative solution module and a broadband signal reconstruction module; A system response estimation module is used to measure the amplitude square response of the analog channel of the critical sampling circuit to be extended, and solve the model coefficient of the amplitude square response to be estimated by minimizing the l1 norm of the difference between the amplitude square response to be estimated and the measured amplitude square response, so as to obtain the frequency response and unit impulse response of the analog channel of the critical sampling circuit; Then, a response matrix of a critical sampling circuit simulation channel is constructed, and rows of the response matrix of the critical sampling circuit simulation channel are extracted to obtain a system response matrix of the critical sampling circuit, which is used for parameter initialization of the extended initialization module; An extended initialization module is used to initialize the parameters of the extended feature iterative solution module using the system response matrix output by the system response estimation module, and input the initialized parameters into the extended feature iterative solution module; The extended feature iterative solution module is used to locate the extended feature most relevant to the current extended residual within the target extended bandwidth in each iteration, use the located extended features to reduce the dimension of the high-dimensional response matrix to obtain a low-dimensional extended feature response matrix, solve the extended feature vector through elastic network regression and update the extended residual, which is used for the extended feature location and residual update of the next iteration, and perform a convergence check on the extended residual or the number of iterations; if satisfied, the solved extended feature vector is input into the broadband signal reconstruction module, otherwise the iteration continues; The broadband signal reconstruction module is used to update the high-dimensional input space using the extended feature vector output by the extended feature iterative solution module, obtain the high-dimensional reconstructed signal in combination with the feature transformation space, perform sampling rate conversion on the high-dimensional reconstructed signal, and obtain the reconstructed signal after the bandwidth of the critical sampling circuit is extended.

Images