Discrete linear canonical txransform of finite chirps

Linear canonical transformation (LCT) as an Fourier transform and fractional fourier transform's generalization, is an effective tool for non-stationary signals and has more flexibility, chirp signal can be looked as a typical nonstationary signal. In this letter, we derived closed-form expressions for the DLCT of a finite chirp. It is shown that the DLCT of a finite chirp is zeros at some points, and the number of zeros is related to chirp rate a, the parameter of DLCT α%, and the root of unity N. And if we choose proper DLCT parameters, the finite chirp is again a finite chirp or the original chirp except for a coefficient.