Research On Time-frequency Transform In Non-stationary Signal

The time-frequency transform is an important method of analyzing non-stationary signals, which provides the joint distribution information of both time-domain and frequency-domain, and clearly describes that how the frequency of signal varies with time, and can give signal instantaneous frequency and amplitude of each moment.This paper takes the time-frequency transform as the research object, based on the depth analysis of the traditional time-frequency transform, mainly studies a time-frequency analysis method----generalized S transform.Firstly, this paper describes the traditional time-frequency analysis methods of short-time Fourier transform, wavelet transform, Wigner-Ville distribution are introduced briefly, and compare the respective advantages and disadvantanges though simulation experiments, the following mainly introduces the basic principle and the derivation process of the S transform.In order to improve the analysis ability of S transform to the non-stationary signal, the generalized S transform is obtained by adding two adjustable parameters to improve the Gaussian window function, and algorithm implementation of the generalized S transform is stated, meanwhile, compare it with other several time-frequency transform methods, the simulation results show that the generalized S transform can get better time-frequency analysis.Secondly, using similar muti-resolution properties of the generalized S transform,the time-frequency filtering method and threshold filtering method based on the generalized S transform have designed in the paper, meanwhile, two methods are applied to de-noising processing of synthetic seismic signal and real seismic signal, the simulation results show that both methods can suppress noise effectively. The generalized S transform can be regarded as the phase correction of wavelet transform, so some theoryof wavelet transform is also applied to the generalized S transform. Based on this, the idea of the wavelet threshold de-noising brings in the two-dimensional generalized S transform, designing the threshold de-noising method based on two-dimensional generalized S transform method. Simulation experiment shows that this method can improve the SNR of image and restrain the noise of the image, it is an effective method of image de-noising.Finally, in order to more conveniently analyze time-frequency of signal with traditional time-frequency transform method and generalized S transform,this paper designs and implements the time-frequency analysis system software based on VC++and MATLAB mixed programming, it provides a rapid and simple test platform for the user.