Research On Improved Time-frequency Analysis Method For Non-stationary Signals

Time-frequency analysis is a powerful tool for non-stationary signal analysis,which can be divided into linear methods and nonlinear methods as well as their respective derivatives.The linear time-frequency analysis method represented by the short-time Fourier transform(STFT)is simple and easy to implement,but the resolution is low,the nonlinear method represented by Wigner-Ville distribution(WVD)is highly aggregated,but the cross-term interference reduces its performance.Over the years,researchers have improved and optimized the characteristics of various methods and proposed many analytical methods,but these methods are mostly based on specific application requirements,and their scope of application still needs to be further expanded.Therefore,based on the theory of existing methods,we still need to continuously improve and explore new methods.Based on the analysis of the characteristics of existing time-frequency analysis methods,this thesis proposes improvements for the shortcomings of different methods.The main works are as follows: 1.In view of the shortcoming of S-transform(ST)which presents as fixed multi-resolution analysis,the standard deviation of the Gaussian window in ST is constructed as a function of time and frequency,which is called the improved generalized S-transform(IGST).After studying the determining factor of Gaussian window standard deviation when the STFT's support domain is minimum,the relationship between STFT and IGST is used to obtain the determinant factor of Gaussian window's optimal standard deviation in IGST.In addition,in order to solve the problem of large estimation error which exists at the frequency intersection of each signal's component in the chirp rate estimating,a frequency recombination method is proposed.Simulation analysis shows that the frequency recombination method can accurately estimate the instantaneous frequency of each signal's component and improve the accuracy of the chirp rate estimation.IGST achieves better signal analysis at different times and frequencies,and has similar anti-noise performance as traditional STFT.2.In order to eliminate the cross-term interference in WVD,the distribution characteristics of the LFM signal's ambiguity function are studied.On this basis,the distribution characteristics of the general non-stationary signal in ambiguity domain are analyzed,and the minimum points around the origin of the ambiguity domain closest to the origin are used as the auto-terms and cross-terms' distribution boundary.At the same time,by combining the edge detection and mathematical morphology,the signal information within the boundary is extracted to restore and reconstruct the signal's time-frequency distribution according to the compressed sensing theory.The simulation results show that the redefined auto-terms distribution area contains more signal auto-terms information,which can be used to recover and reconstruct the time-frequency distribution with higher aggregation.In addition,compared with the traditional time-frequency analysis methods,the new method has stronger anti-noise performance.3.After studying the characteristics of common parameterized time-frequency analysis methods,the generalized parameterized time-frequency analysis(GPTFA)method is proposed to avoid the problem that the non-parametric time-frequency analysis method has low time-frequency aggregation.In addition,based on signal frequency recombination,a multi-component signal separation method is proposed.The simulation shows that compared with the non-parametric method,the parameterized time-frequency analysis method can obtain a more aggregated time-frequency distribution when the parameter approaches the theoretical value.The signal separation method proposed in this thesis can achieve multi-component signal separation,and the separation results are superimposed to obtain a highly aggregated time-frequency distribution of the multi-component signal.Finally,due to the use of iterative estimation for better parameter estimation performance,the GPTFA method can still obtain a high-aggregation time-frequency distribution in a low SNR environment.