Study On Random Sampling Model And Its Signal Processing Algorithm

With the development of electronic information technology and the rapid growth of data needs,the signal acquisition technology based on the Shannon-Nyquist sampling theorem brings a great challenge to signal processing capability and hardware.The introduction of random equivalent sampling breaks the restriction of traditional sampling theorems.On the basis of in-depth analysis of random sampling model,this paper studies the uncertainty of sampling time and optimizes the design of sampling model.Combined with the theory of compressed sensing,the time domain and frequency domain processing algorithms of sampled signals are studied.The main research work is as follows:1.Study on sparse signal reconstruction algorithm based on sequential equivalent time sampling.Firstly,based on the optimized random sampling model,the characteristics of the applied signal of sequential equivalent time sampling and compressed sensing theory are analyzed in the time domain.Then,the compressed sensing theory is used to improve the reconstruction methods of random sampling signal and the periodic non-uniform sampling signal.Combined with the Shannon interpolation formula,a compressive measurement matrix suitable for the sequential equivalent time sampling and periodic non-uniform sampling is constructed.Finally,a signal reconstruction algorithm of the sequential equivalent sampling based on CS is designed.The algorithm reconstructs the random sampling signal in frequency domain,and achieves more accurate reconstruction signal,and effectively reduces the number of random sampling and improves the sampling efficiency.2.Study on power spectrum estimation algorithm.In practical signal processing,it is inefficient and unnecessary to use a lot of times to random sampling to reconstruct the entire original signal waveform.Based on the random equivalent sampling model proposed in this paper,the relationship between the spectrum of random sampling signal and the spectrum of original signal to be reconstructed is analyzed.The compressed sampling method is used to solve the autocorrelation matrix established in the time domain,the power spectrum estimation uses least square method and CS method is adopted respectively.Finally,the feasibility of the two algorithms is evaluated through experimental simulation.3.Study on the sub-Nyquist sampling based on random triggered.In this study,a random triggered modulation wideband converter sampling model is proposed in the sub-Nyquist sampling system,the problems such as low reconstruction performance of MWC sampling technique are solved.The sampling model is different from the random equivalent sampling model for line spectrum signal.It is applicable to both the sparse multi-frequency signal and the line spectrum signal.In this study,the above two signals are reconstructed based on the random triggered sub-Nyquist sampling model,and the feasibility of reconstructing the signal by the sampling model is verified through the experimental simulation.