Noise Analysis On Discrete Linear Canonical Transform

As a general form of Fourier transform,the linear canonical transform(LCT)was introduced in 1970 s.LCT has its unique advantages and it is better in non-stationary signal processing than Fourier transform,therefore,more and more researchers focus on the LCT.As LCT is widely used in many subjects,many kinds of definitions and implementation of the discrete LCT(DLCT)have been derived in.To use the results of these algorithms in an efficient way,it is necessary to know the value of signal in the LCT domain due to the noise disturbance associated with the noise influence in the LCT domain.It is therefore interesting and worthwhile to investigate the noise influence after DLCT.In this paper,the properties of noise after a DLCT are analyzed.The main contributions and innovations of this dissertation are summarized as follows:(1)Show the definition of LCT and DLCT.Then introduce the knowledge of chirp signal and the Central Limit Theorem.(2)Make some assumptions on noise and prove the noise on the LCT domain can be approximately modelled as Gaussian in theory.Then calculate the mean and covariance matrix of noise and the general trend of the noise after DLCT is described.(3)Introduces two special cases: one is the case when DLCT reduces to DFT,and compare with the derived theory about noise on FT domain.Another is the case when noise is white Guessian noise(WGN)and make the proof that WGN is still WGN after DLCT.(4)Simulations on many aspects verify the proven theories and finally talks about some potential applications.