Theory and applications of short-time linear canonical transform

Abstract The linear canonical transform (LCT) is a powerful tool for signal processing and analyzing the non-stationary signals. However, it fails to process the signals whose linear canonical frequencies change over time due to the lack of time localization information. In this paper, we use the short-time linear canonical transform (STLCT) to solve this problem. First, its one-dimensional and two-dimensional inverse transformations are derived. Also, we derive some basic properties and the convolution theorem. Then, we also provide the time-canonical-frequency analysis of this transform. Finally, we give the discrete form and filter interpretation of STLCT. Moreover, we study practical applications of STLCT in time-frequency analysis of chirp signals. The simulation results show that the time-frequency resolution of STLCT is better than that of short-time Fourier transform (STFT), wavelet transform (WT) and generalized S transform (GST).