Research on Sub-Nyquist Rate Sampling Method Based on Sparse Fourier Transform Theory

With the development of information technology, the amount of data of the signal acquisition end in high sampling rate fields such as wireless communication and medical imaging based on the Nyquist sampling theorem has increased dramatically. The resulting intensive data processing brought great challenges to the data collection, storage, and transmission of the system. Researchers began to focus on the “sparse” characteristic of the signal, hoping to see the whole from the small, and develop a more efficient signal processing method. Recent studies showed that the Sparse Fourier Transform algorithm can achieve sublinear Fourier transform based on the “sparse” characteristic of signals in the frequency domain. In this paper, based on the theoretical research and application development of Sparse Fourier Transform in recent years, the basic theoretical framework of Sparse Fourier Transform, frequency basket, subsampling Fast Fourier Transform, and other key technical problems and classical reconstruction algorithms are summarized. And an offline method is used to verify that, in the sampling process of one-dimensional random signals which are sparse in the frequency domain, the sampling rate of the subsampling method based on Sparse Fourier Transform is reduced to 1/27 compared with that of the traditional Nyquist sampling, and the recovery error is less than 10e-14 in the case of no noise, thus successfully completing the compression in the signal acquisition process.