Linear Canonical Stockwell Transform: Theory and Applications

The Stockwell transform (ST), which is a reversible method of time-frequency spectral representation, is an extension of the ideas of the wavelet transform (WT) and short-time Fourier transform (STFT). And yet, it represents the signal just in the time-frequency plane, which is unfavorable for nonstationary signals. In this paper, a new linear canonical Stockwell transform (LCST) is proposed based on the specific convolution structure in linear canonical transform (LCT) domain, which is a combination of the merits of ST and LCT to address this problem. It not only characterizes the signal in the time-linear canonical frequency plane, but more importantly, inherits the advantages of ST with a clear physical meaning. First, the theories about the continuous LCST are described at length, including its definition, basic properties and the time-LCT domain-frequency analysis. Next, the convolution theorem and cross-correlation theorem constructed in LCST domain are considered. Further, the discretization algorithm of the LCST is explored in order to realize it in the physical system. Finally, based on the proposed LCST, we study and discuss several applications of it, including time-frequency analysis and filtering of chirp signals. The rationality and validity of the work is verified out by simulations.