Linear Canonical Stockwell Transform and the associated Multiresolution Analysis

TL;DR

This paper introduces the linear canonical Stockwell transform (LCST), explores its fundamental properties, and develops a multiresolution analysis with an orthonormal basis for L^2(R), advancing the mathematical framework of signal analysis.

Contribution

It provides a new definition of LCST, analyzes its properties, and constructs a multiresolution analysis with an orthonormal basis, expanding the theoretical tools for signal processing.

Findings

LCST range is a reproducing kernel Hilbert space

Reconstruction formula for LCST established

Orthogonal basis for L^2(R) constructed

Abstract

In this article, we give a new definition of the linear canonical Stockwell transform (LCST) and study its basic properties along with the inner product relation, reconstruction formula and also characterize the range of the transform and show that its range is the reproducing kernel Hilbert space. We also develop a multiresolution analysis (MRA) associated with the proposed transform together with the construction of the orthonormal basis for $L^2(\mathbb{R}).$