Short-time Linear Canonical Transform Based Time-frequency Analysis For Non-stationary Signal

Most of the signals produced in complex industrial processes have non-stationary characteristics.For example,fault detection and diagnosis in wind power grid connected systems are faced with large numbers of non-stationary signals.It cannot get good results in single time domain analysis or frequency domain analysis of non-stationary signals because its parameters change with time.The short-time Fourier transform(STFT)is one of the most effective methods of time-frequency joint analysis for non-stationary signals.The linear canonical transform(LCT)and the offset linear canonical transform(OLCT),generalized form of the Fourier transform(FT),are novel signal processing methods developed rapidly in recent years.However,they are the same as the FT,which is a global transformation.That is the relation between time and frequency of signal cannot be reflected.Therefore,this thesis focuses on time-frequency analysis theory based on short-time linear canonical transform(STLCT).However,as a new time-frequency analysis tool,the STLCT is still at the initial stage in the field of non-stationary signal processing.Many basic problems,such as the choice of window function and the time-frequency properties,have not been studied yet.The solution of these problems will be important for the future application of time-frequency analysis tools in practical engineering.In this thesis,we take the non-uniform sampling problem of OLCT as an entry point,and analyze the advantages and disadvantages of it and the LCT.Time-frequency analysis method based on STLCT is mainly studied.The main contents of this thesis are as follows:Nonuniform sampling theorems in the OLCT domain are proposed.The problem of uniform sampling in the LCT and OLCT domain has attracted much attention by scholars.However,due to the fact that the sampling equipment in the engineering cannot achieve uniform sampling,there is always an error of sampling time.And the signals received by some sensors have strong random characteristics.To tackle these problems mentioned above,the nonuniform sampling theorems for deterministic signals and random signals in the OLCT domain are investigated.Based on the analysis of typical nonuniform sampling models,nonuniform sampling theorems in the FT domain are extended to the OLCT domain by generalized kernel function,Expanding the scope of the sampling method of the OLCT.Time-frequency distribution properties and optimal window selection for the STLCT are proposed.Aiming at researching that both the LCT and OLCT cannot reflect the relationship between time and frequency,we study the windowed form of the LCT and its time-frequency properties in signal processing.Some basic properties of time-frequency distribution including time shift,frequency shift,2-D resolution and finite support of time-frequency plane are studied in this chapter.The computation method,inverse form,and the selection of optimal window function are also studied.And the result that Gaussian window function is the optimal window function of the STLCT is obtained.Finally,the simulations verify the correctness of the proposed properties and result.Spectrum analysis and uncertainty principle in the STLCT domain are proposed.Since the uncertainty principle is one of the most significant principles in signal processing,the uncertainty principle of LCT has attracted much attention by many scholars.However,the uncertainty principle in one STLCT domain has not been studied.In this thesis,from the perspective of relationship between the traditional FT and STFT,we focus on the uncertainty principle in the one STLCT domain,getting the results that the uncertainty principle in one STLCT domain are consistent with the results in the LCT domain,but they have different implications.The relationship between the uncertainty principle and spectrum in the STLCT domain is also analyzed.Dual window computation for the short-time linear canonical series expansion is proposed.Time-frequency analysis method based on STFT was proposed by Gabor in 1946.But it is difficult to calculate its coefficients because the basis function of Gabor series expansion is non-orthogonal.So its application was limited at that time.Gabor expansion did not attract much attention by scholars until the bi-orthogonal condition was proposed.As a generalized form of Gabor expansion,the problem of non-orthogonal basis function of the short-time linear canonical series expansion is also inevitable.To solve this problem,in this thesis,first,orthogonal condition and its corollaries of the OLCT are derived by generalizing the bi-orthogonal condition of the traditional Gabor expansion.Second,based on the derived corollaries,dual window of the short-time linear canonical series expansion can be calculated by energy minimization method,which has a good approximation of the original window function.Its validity is proved by simulation.Finally,influences of free parameters to shape of dual window are studied,which provide a prerequisite for application of short-time linear canonical series expansion.Finally,based on the study of the above problems,a summary and prospects for future directions are given in the last chapter of this thesis.