Research On Adaptive Time-frequency Analysis Algorithm For Non-stationary Signals

As an important method to analyze non-stationary signals,time-frequency analysis(TFA)can provide comprehensive information of a signal on the time and frequency domain.The method can describe the relationship between signal frequency and time clearly,and also gives the instantaneous frequency and amplitude of a signal at each individual time.The main focus of this paper is to address the low time-frequency aggregation and poor self-adaptation problems of traditional time-frequency analysis methods.This paper mainly studies the adaptive short-time Fourier transform algorithm and adaptive time-frequency synchronous compression algorithm,and applies them to solve the problems of parameter estimation and multi-component signal separation.Firstly,this paper introduces the mathematical models and time-frequency characteristics of common non-stationary signals,including LFM signals,SFM signals and frequency hopping signals,and analyzes the synthesized signals with traditional time-frequency analysis methods.Besides,the Renyi entropy is used as the evaluation index to compare their time-frequency aggregation performances.Simulation results show that the Renyi entropy of the synchronous compression transform is the smallest and its time-frequency aggregation performance is the best when the signal-to-noise ratio locates between 0d B and 25 d B.On contrast,the Renyi entropy of the short-time Fourier transform is the largest and its instantaneous frequency aggregation performance is the worst.Secondly,consider that the linear time-frequency analysis method is limited by the uncertainty criterion,and has the problem of low time-frequency resolution and timefrequency aggregation,the adaptive short-time Fourier transform algorithm is introduced in this paper.In order to enable the signal to achieve good aggregation characteristic in the time and frequency domains,the time domain and frequency domain adaptive STFT methods are designed,where the time domain adaptation is based on the instantaneous frequency rate and the frequency domain adaptation is based on the concentration measure.The time domain adaptation method firstly obtains the instantaneous frequency of the signal through the spine of wavelet transform,and using the instantaneous frequency rate to get the adaptive window length of the signal.Simulation results show that the algorithm improves the time-frequency aggregation of the signal.When it is used to estimate the insantanesous frequency of frequency hopping signals,the MSE of frequency estimation is less than 0.08 at-8d B signal to noise ratio.The frequency domain adaptive STFT is based on the concentration measure.In this dissertation,we have used three different concentration measures,and their appropriateness for the signals is demonstrated by simulation results of singlecomponent and multi-component signals.Finally,in order to overcome the shortcomings of existing TFA methods,based on the adaptive short-time Fourier transform algorithm,the adaptive time-frequency simultaneous compression(AFSST)algorithm is introduced in this paper.Specifically,the adaptive second-order time-frequency simultaneous compression(AFSST2)algorithm is introduced to deal with signals with rapid frequency changes.Simulation results show that AFSST2 has a good time-frequency aggregation performance.In order to improve the time-frequency aggregation and not to affect the signal reconstruction performance,the AFSST2-WVD algorithm is proposed.And it is shown that the proposed algorithm can reconstruct the signal while maintaining the higher timefrequency aggregation than other time-frequency synchronous compression algorithms.