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Modelling the noise influence associated with the discrete linear canonical transform

In this study, the properties of noise after a discrete linear canonical transform (DLCT) are analysed. First, the authors prove that the DLCT of noise can be modelled by a Gaussian distribution with very weak assumptions on the noise in the time domain. Then, the mean and covariance matrix of this Gaussian distribution is derived and the general trend of the noise after DLCT is described. In addition, they find that the properties of noise in the LCT domain are the generalisation of the properties of noise in the Fourier transform domain. What is more, the authors prove that the additive white Gaussian noise (AWGN) is still an AWGN after performing the DLCT. Finally, the simulations are performed to verify the effectiveness of the obtained results.