Research On Discrete Gabor Transform Algorithm With High Aggregation Degree

Time-frequency analysis plays an indispensable role in the field of signal processing.The joint distribution of time and frequency can directly display the characteristics of signal frequency changing with time.For the analysis and processing of common non-stationary signals in practical application,it is more reasonable and effective than pure time-domain analysis or frequency-domain analysis.The mainstream time-frequency analysis methods can be roughly divided into linear,bilinear and parametric time-frequency analysis.Bilinear timefrequency analysis is easy to be affected by cross interference terms.Although parametric timefrequency analysis can eliminate cross interference terms,the calculation complexity of calculating the parameters of basis function model is high.In contrast,linear time-frequency analysis not only has no cross interference term,but also has simple calculation and easy implementation,which makes the research of linear time-frequency analysis method more extensive.In the research of linear time-frequency analysis method,Gabor transform has important research value and significance.In recent years,there are many researches on Gabor transform.Compared with the algorithm research of obtaining the dual window of Gabor transform and the fast algorithm research of Gabor transform,the algorithm to improve the time-frequency accuracy and timefrequency aggregation of Gabor transform has always been the focus of research.On the premise of displaying all frequency components of non-stationary signal,improving the accuracy and aggregation of time spectrum can be better used in practice.This thesis mainly studies and improves the single window and linear combined window discrete Gabor transform based on the high concentration of time spectrum.The research contents are as follows:(1)The width of window function is closely related to the time-frequency aggregation of single window discrete Gabor transform.Aiming at the problem that the optimal window width appears peak preference and the algorithm has poor anti noise performance when the window width of single window discrete Gabor transform is adaptively selected based on the norm of transform coefficient,Rayleigh entropy and Shannon entropy,a window width algorithm of single window discrete Gabor transform based on improved Shannon entropy is proposed in this thesis.Firstly,taking the aggregation degree of the transformation coefficient as the variable,the Shannon entropy is calculated after normalization,so that the adaptively selected window width is more inclined to the spectrum with high aggregation degree.Then,by improving the value range of Shannon entropy,the time-frequency aggregation degree can be judged directly according to the value of improved Shannon entropy.Finally,the improved Shannon entropy of the transformation coefficients corresponding to all window functions from the minimum window width to the maximum window width is calculated.The window width corresponding to the maximum Shannon entropy is the optimal window width.When dealing with nonstationary signals,the algorithm can not only display all components,but also improve the timefrequency aggregation and time-frequency accuracy,and has good anti noise ability.(2)The traditional single window and multi window discrete Gabor transform algorithms often can not effectively display all the frequency components in the signal when analyzing and processing the signal containing different time-frequency components,and the time spectrum aggregation and accuracy are not high.However,the current linear combined window discrete Gabor transform method has poor anti-noise performance and high computational complexity,which can not meet the requirements of practical application.For these problems,based on the correlation between the sparsity of transform coefficients and time-frequency accuracy and time-frequency aggregation,a linear combined window discrete Gabor transform algorithm based on the sparse solution constraint of transform coefficients is proposed in this thesis.Firstly,based on the idea of the adaptive selection algorithm of the optimal window width of single window discrete Gabor transform proposed in this thesis,an adaptive selection method of the optimal number of window functions is proposed.A group of window functions with different window widths are selected to obtain the sparse solution of the transformation coefficients,and the best linear combination coefficients are obtained by the gradient descent method.Secondly,according to the best linear combination coefficient,all window functions are combined into analytical window functions.Finally,the influence of important parameters on the combined window algorithm is further studied.The results show that the number of window functions has a great influence on the algorithm,and the influence of regularization parameters can be ignored.The experimental results of simulated non-stationary signal and real ECG signal show that the algorithm can display all frequency components of the signal,and the time-frequency accuracy is improved by 3% to 10%.At the same time,the anti-noise performance is improved by 20%compared with the current linear combination window algorithm,which can meet the needs of practical application.