Research On Time-Frequency Analysis Of Multicomponent Non-Stationary Signals

The signals in nature such as seismic signals,speech signals and biomedical signals are all non-stationary signals.In order to understand the information behind,it is very important to find a tool for analyzing non-stationary signals.Time-frequency analysis is widely concerned because it can express both the time and frequency information of the signal at the same time.With the development of technology,the time-frequency analysis technology of single component signals is mature,which is mainly due to the absence of the cross term.Therefore,Wigner-ville distribution(WVD),Teager energy operator,and parameterized time frequency distribution are all suitable for this kind of signal.So the focus of this paper is the time-frequency analysis of multi-component signals.There are so many kinds of time-frequency analysis methods.Through the review on the existing algorithms,this paper divides the existing algorithms into two major categories:parametric and non-parametric.Three improvements are investigated as follows:(1)There are two ways to explain the Short time Fourier transform(STFT):the transform viewpoint and the filtering viewpoint.The transform explanation is well known by the public where STFT is the Fourier transform of windowed signal frames.Due to the uncertainty principle of Heisen-Berg,it can not achieve good resolutions of both frequency and time at the same time.While according to the filtering viewpoint,the frequency resolution is just controlled by the number of channels selected,and the time resolution can be as high as the sampling interval.In addition,there is no restriction on the impulse response length of the filter or the length of the selected signal segment.By studying the filtering STFT of the LFM signal,it is found that the filter length of the filter bank will change the time-frequency concentration of the time-frequency surface.For the linear frequency modulated(LFM)signal with certain modulation parameter,as the filter length grows,the time-frequency concentration will increases first and then decreases.It means there is the most appropriate filter length that provides the highest time-frequency concentration for each LFM signal.Meanwhile,it is also found that the smaller the modulation parameter is,the longer the optimal impulse response length is.Therefore,if the approximate frequency range of the studied signal is known beforehand,the most appropriate filter length can also be selected in advance in order to get the highest time-frequency concentration.If the signal studied is a multi-component signal,inspired by the previous algorithm,the filtering STFT can be combined with the WVD.(2)The parameterized time-frequency distribution is mainly proposed for the single component signal.Though scholars have tried to improve the algorithm to make it applicable to the multi-component situation,the computation is still large,and the corresponding prior information still needs to be obtained manually.This inevitably restricts the wide application of the parameterized time-frequency distribution.In this paper,it is found that if the parameters of the estimation are not suitable,the time-frequency concentration of single component signal is very low.Therefore,for multicomponent signal,after obtaining the frequency modulation parameters of each component,the superposition algorithm is put forward to get the high time frequency concentration.(3)The parameter estimation of the parameterized time-frequency analysis in each step is mainly based on the extracted ridge edge of the time-frequency surface.This will be greatly affected by the noise,especially when the studied signal is of multicomponent,which in turn gives the time frequency distribution result of bad concentration.In this paper,the Hough transform,commonly used in the field of image processing,is used to take the placed of ridge extraction and fitting.It is shown that the Hough transform can still provide not only more accurate parameter estimations at the lower SNR,but also the multi-parameters for multicomponent signals.(4)The above two algorithms are mainly applicable to the multicomponent LFM signals,but not suitable for Nonlinear FM signals.Through the study of the parameterized time-frequency distribution,it is also found that the main difficulty of the parameterized time-frequency distribution is to divide the regions of each component.The previous algorithm takes the simple manual division,which restricts the practical application of the algorithm.This paper introduces the concept of connected domain to have an automatic region division.Since in the experiment,errors show up at the intersection between the frequency trajectories of signal components,the WVD,which has serious cross term interference for the multicomponent signals,is adopted for its defect in searching for the cross points.Because of the existence of the cross term,the amplitude of the intersection points must be very high.We can find the intersection point and pretreat it according to this characteristic.