Research Of Sparse Frequency Estimation For Sub-Nyquist Sampling Signal

In recent years, research on the sparse frequency signal parameter estimation caused wide-spread focus and concentration. However, it is difficult to sample the wide band signals at Nyquist sampling rate , sub-sample technology is one way to solve this problem. How to maintain the high probability of frequency sparse signal at low signal to noise rate , is the content of this paper.This paper focused on the sub-nyquist sampling of sparse freqnency signal to estimate its frequency. First the compressed sensing theorem is proposed, together with its application in the spectrum estimation field. The paper next mentioned a new approach of Fast Fourier Sample algorithm, based on random sampling idea. The algorithm uses non-uniform FFT method and few correlative random samples of initial signal to high efficiently estimate its DFT expression. Some improvements have done by the writter. Some analysis as well as computer simulation are provided in the end of this capture. In the third capture, a robust reconstruction algorithm called robust Chinese Remainder Theorem (CRT) is proposed, when the remainders have errors. It showed that with the robust CRT, the sampling frequencies can be significantly reduced, and it can be applied in the field of single or multi frequency estimation field.In the end of this paper, comparative work is done by using the three methods proposed the discrete application in frequency estimation, made a conclusion and pointed the next orientation of the further study. These methods this paper proposed are a good way to be used in the field of DOA estimation, SAR image and Doppler decomposition on radar signal processing field.