Sampling theorem for the short-time linear canonical transform and its applications

In this paper, we propose a sampling theorem for the short-time linear canonical transform (STLCT) by means of a generalized Zak transform associated with the linear canonical transform (LCT). The sampling theorem, which states that the signal can be reconstructed from its sampled STLCT, turns out to be a generalization of the conventional sampling theorem for the short-time Fourier transform (STFT). Based on the new sampling theorem, Gabor׳s signal expansion in the LCT domain is obtained, which can be considered as a generalization of the classical Gabor expansion and the fractional Gabor expansion, and presents a simpler method for reconstructing the signal from its sampled STLCT. The derived bi-orthogonality relation of the generalized Gabor expansion is as simple as that of the classical Gabor expansion, and examples are proposed to verify it. Some potential applications of the linear canonical Gabor spectrum for non-stationary signal processing are also discussed.