Sampling Techniques and Error Estimation for Linear Canonical S Transform Using MRA Approach

Abstract

A linear canonical S transform (LCST) is considered a generalization of the Stockwell transform (ST). It analyzes signals and has multi-angle, multi-scale, multiresolution, and temporal localization abilities. The LCST is mostly suitable to deal with chirp-like signals. It aims to possess the characteristics lacking in a classical transform. Our aim in this paper was to derive the sampling theorem for the LCST with the help of a multiresolution analysis (MRA) approach. Moreover, we discuss the truncation and aliasing errors for the proposed sampling theory. These types of sampling results, as well as methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.

Keywords

• linear canonical S transform (LCST)
• multiresolution analysis (MRA)
• sampling theorem
• error estimation