The S-Transform and Its Inverses: Side Effects of Discretizing and Filtering

The aim of this paper is to present a study on the potential and limits of the -transform and its inverses. The S-transform is an extension of the short-time Fourier transform with characteristics of the wavelet transform. It is mostly used for time-frequency analyses. Two different inverse S-transforms have been presented in the literature. We explain why the most recent one is an approximation but a very good one. The level of approximation is calculated in this paper. We then discuss the relative merits of both inverses. A careful study enables us to show that, although both inverses are nearly exact in the infinite continuous domain, this is not true anymore in the practical finite discrete domain. Side effects are quantified, and typical examples are given. Time-frequency filtering is one of the main applications of the S-transform. We evaluate the effects that occur when using the S-transform and its inverses for filtering.