Research On The Theory And Applications Of Linear Canonical S Transform

Chirp signal is a kind of non-stationary signal that exists widely in nature and engineering fields,and time-frequency analysis is a powerful tool for non-stationary signal processing.As the generalized form of Fourier transform,linear canonical transform can be regarded as the decomposition form of chirp bases,so it has advantages in processing chirp-like signals.However,the kernel of the linear canonical transform is a global kernel function,which cannot characterize the local characteristics of the signal.The S transform can analyze the signal in the time-frequency plane and also has the advantage of multiresolution analysis.However,since the kernel function of S transform has a time-invariant frequency and does not have good time-frequency concentration,it is not suitable for processing time-varying signals.Although there have been many improved S transforms,these methods still process the signal in the Fourier domain.Therefore,for the signal whose energy is not concentrated in the Fourier domain,the result obtained by the S transform is not optimal.Therefore,the combination of linear canonical transform and S transform can characterize signals in the time-linear canonical frequency domain,which is more conducive to processing nonstationary signals.Based on the S transform and linear canonical transform,this paper proposes the linear canonical S transform and applies the theory to chirp signal processing.Compared with the existing linear canonical S transform,the new linear canonical S transform proposed in this paper has a simpler definition structure and better inherits the advantages of the S transform.More importantly,it has a clear physical meaning.The specific work is summarized as follows:The first part constructs a new linear canonical S transform.This new time-frequency analysis tool is proposed by considering the S transform as a phase-corrected wavelet transform,combined with the linear canonical domain convolution theorem.First,explore its basic properties,the principle of uncertainty,and its connection with other distributions.In addition,it analyzes its time-linear canonical frequency domain analysis capabilities from two aspects: constant Q and time-linear canonical frequency domain resolution.Secondly,discretize the parameters of the linear canonical S transform,and obtain the reconstruction formula of the discrete linear canonical S transform through the constructed linear operator.Furthermore,the linear canonical S transform is used to analyze the almost periodic function,and the generalized frame decomposition of the almost periodic function is constructed.Finally,the simulation of time-frequency analysis of chirp signal proves that the proposed new transform has good time-frequency concentration.The second part proposes the generalized linear canonical S transform.This definition starts from the generalized S transform,which regards the S transform as a special short-time Fourier transform,and is proposed in combination with the linear canonical domain convolution theorem.First,explore its basic properties,and analyze its time-linear canonical domain analysis ability from the time-linear canonical frequency domain resolution.Secondly,construct the convolution theorem and correlation theorems of the generalized linear canonical S transform domain.Furthermore,the discrete algorithm in the linear canonical domain and time domain related to the generalized linear canonical S transform are proposed.Finally,the use of chirp signal time-frequency analysis simulation verification proves the effectiveness and advantages of the proposed linear canonical S transform.The third part applies the generalized linear canonical S transform to chirp signal processing.First,time-frequency analysis is performed on the chirp signal and the noisy chirp signal to prove the effectiveness and advantages of the generalized linear canonical S transform.Further,explore the detection ability of the generalized linear canonical S transform on the interfered chirp signal,and prove its advantage in anti-interference.Secondly,a time-linear canonical domain filter based on generalized linear canonical S transform is constructed,and its effectiveness is proved by the application of signal component extraction.In addition,it is applied to the filtering of noisy chirp signals to prove its advantage in signal denoising.Finally,in order to prove that the proposed new time-frequency analysis tool has potential for real-world signal processing,time-frequency analysis and verification of bat echolocation signals are carried out.