Research On Equivalent Sampling And Sparse Reconstruction Algorithm Of High Speed Signal

With the rapid development of modern information transmission,the requirements of signal acquisition and processing system are also increasing.The existing ADC sampling devices are usually limited by Shannon Nyquist sampling theorem.With the continuous improvement of signal transmission rate,the sampling rate and sampling accuracy of the existing ADC can't meet the requirements of high-speed signal real-time acquisition.Equivalent sampling effectively breaks through the limitation of Shannon Nyquist sampling theorem by using the periodicity of signal,therefore,it solves the problems existing in high-speed signal acquisition of existing ADC.However,this method still needs a lot of sampling data to accurately reconstruct the original signal,which leads to the high cost of sampling reconstruction time.In this paper,the equivalent sampling reconstruction method combined with signal sparse reconstruction algorithm is used to solve the above problems.The main research work of this paper is as follows:(1)The existing equivalent sampling reconstruction method can achieve high equivalent sampling rate,using low-speed ADC,but still need a lot of sampling data for signal reconstruction.Therefore,this paper studies a reconstruction method of pseudo-random equivalent sampling signal based on matrix completion.In this method,the observation matrix is constructed by selecting part of the sampled data after the equivalent sampling by pseudo-random method.However,the matrix can't effectively satisfy the strong incoherence of matrix completion,and can't directly complete the missing data.Therefore,the Hankel transform is used to transform the matrix to satisfy the strong incoherence condition of matrix completion.Then,the complete observation matrix is obtained by filling some missing data in the observation matrix with matrix completion algorithm,and the reconstructed original signal is finally obtained by Hankel inverse transformation.In this algorithm,the original signal is reconstructed by using part of the signal data in the equivalent sampling,and the number of equivalent sampling is reduced,thus the time cost of the reconstruction of the equivalent sampling signal is effectively reduced.(2)In the reconstruction method of equivalent sampling signal based on matrix completion,Hankel transformation is needed for the matrix,and the original signal is obtained through the reconstruction of IALM algorithm,which increases the computational complexity.Therefore,this paper studies a pseudo-random equivalent sampling signal reconstruction method based on OMP algorithm.In this method,the signal is represented sparsely in the discrete Fourier domain,and the observation matrix is constructed by Whittaker Shannon interpolation formula to build the sparse reconstruction model.The OMP algorithm in thecompressed sensing theory is selected to reconstruct part of the sampled data signals completely and accurately.The algorithm can reconstruct the original signal more accurately with less sampling data,and improve the efficiency of sampling reconstruction.(3)In order to improve the accuracy and efficiency of sampling reconstruction,an equivalent sampling signal reconstruction method based on SL0 algorithm is proposed.In this method,the sparse basis and observation matrix of the equivalent sampling signal reconstruction method based on OMP algorithm are used,and the sparse reconstruction model is established.The approximate approximation norm of smooth continuous function is selected to convert the solution to the original signal.The algorithm can reconstruct the original signal more accurately with less sampling data,which further improves the efficiency of sampling reconstruction.