Application of wavelet and Fourier transform in  time series analysis

Exactly decomposing the feature information of time series is the precondition to nonlinear variation analysis. According to the characteristics of Fourier and wavelet transform, two methods are integrated and applied to analyze time series in time domain and frequency domain, and comprehensive algorithm of wavelet and Fourier transform is presented. Firstly, the wavelet function DB4 is used to decompose the coordinate time series into five layers to get the high frequency and low frequency parts. Then, the time domain waveforms of each harmonic and the possible sudden change information and intervals are obtained. Finally, the exact frequency and amplitude of each harmonic are obtained on the basis of fast Fourier transform. The results show that the low-frequency analysis can intuitively obtain the “annual term” and “two-year cycle term”, while the high-frequency analysis is consistent with the extraction of short-term cycles such as “semiannual term” and “one-season term”. So the method based on wavelet transform and Fourier transform has many advantages compared with Fourier transform and wavelet transform alone, it can effectively extract the feature information of station time series, and has a big research value.