Research And Application Of Wavelet Time-frequency Synchrosqueezing Transform Method

As an important method of non-stationary signal processing,time-frequency analysis provides the joint distribution information of both time-domain and frequency-domain,and clearly depicts 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 analysis as the research object,based on the depth analysis of traditional time-frequency analysis methods,mainly studies the time-frequency analysis method of synchrosqueezing continuous wavelet transform and applied to solve the problem of time-frequency aggregation,separation and instantaneous frequency estimation of multicomponent non-stationary signals.Firstly,aiming at the defect of multicomponent non-stationary signal processing with the existing time-frequency analysis method,such as the inability to achieve better results in energy aggregation,cross-interference term influence and reversibility,this paper introduces the concept of synchrosqueezing transform(SST)on the basis of continuous wavelet transform(CWT).In order to make the non-stationary signals aggregate well at both high and low frequencies,we put forward the adaptive CWT,WSST and second-order WSST(WSST2)distribution,and have carried on the theoretical analysis and formula derivation.In order to select the adaptive parameters which make the time-frequency distribution aggregate better,an adaptive parameter estimation algorithm based on local Rényi entropy is proposed on the basis of global Rényi entropy.The superiority of the proposed method demonstrated through the simulation experiment results.Secondly,the traditional harmonic analysis method,Fourier transform,can not reliably and accurately represent the non-stationary signals,and empirical mode decomposition(EMD)lacks a unified mathematical basis,which will cause a series of problems such as mode confusion and false signals.In this paper,a time-frequency analysis method based on local adaptive harmonic model is introduced.Considering that the multicomponent signals can not be separated effectively when the single-frequency model is used to approximate the signals locally.The linear frequency modulation(LFM)is proposed to locally approximate and modify the signal.It improves the analyzability conditions,so as to meet the needs of actual signal processing.At the same time,from the mathematical theory,a detailed derivation process of the formula is carried out.However,in practical applications,the prior information of signals is generally unknown.So an estimation algorithm of time-varying parameters is proposed to estimate the separated time-varying parameters.The simulation results show the reliability and robustness of the proposed signal separation theory and the time-varying parameter estimation algorithm.Finally,to overcome the shortcomings of existing instantaneous frequency(IF)estimation methods for multicomponent non-stationary signals,an IF estimation algorithm based on WSST2 and Viterbi is proposed.It guarantees that WSST2's high time-frequency aggregation and Viterbi's optimal path selection can be fully utilized.The combination of the two methods makes IF estimation more accurate.According to the different existence forms of multicomponent non-stationary signal,the IF estimation algorithms in corresponding cases are discussed respectively.The simulation results show that the proposed IF estimation algorithm is effective.