Study Of The Application Sparse Fast Fourier Transform

Currently,the most commonly used algorithm for computing the Fourier Transform is the Fast Fourier Transform algorithm.The sparse Fast Fourier Transform algorithm is based on the sparsity of the signal in frequency domain.By using some sampling points,the original spectrum of the signal can be reconstructed with high efficiency and probability.This algorithm is 10~100 times more efficient than the traditional Fast Fourier Transform algorithm.The performance improvement is an approximate linear algorithm.The sparse Fast Fourier Transform algorithm shows great potential applications in data processing in radar,wireless communication,medical imaging,seismic data.Data of tidal gauges,water level stations,and IGS stations,are sparse in the frequency domain.The sparse Fast Fourier Transform is based on the sparsity of signals,i.e.,the contribution of most frequencies to the overall signal is negligible.This paper deals with the data of tide gauge and water level station to verify the performance of sparse Fast Fourier Transform algorithm for fast computation and filtering,and analyzing the coordinate time series of CORS station.The main content of this paper is summarized as follows:(1)The development and application of sparse Fast Fourier Transform algorithm are summarized.The sparse Fast Fourier Transform is described in detail,and the influence of error is analyzed.(2)The basic theory of time series is introduced,and the common methods of time series analysis are elaborated.(3)The sparse Fast Fourier Transform algorithm was used to analyze the spectrum of tide gauge stations,water level stations,and IGS stations,and compared with the spectrum of the Fast Fourier Transform analysis.The results showed that the combination of sparse Fast Fourier Transform and Inverse Fourier Transform method can be used to the filtering on time series data.The spectrum obtained by sparse Fast Fourier Transform can be extended to make short-term prediction of time series.The prediction is better than the traditional polynomial fitting.