Special Affine Stockwell Transform Theory, Uncertainty Principles and Applications

TL;DR

This paper introduces the special affine Stockwell transform (SAST), combining affine Fourier and Stockwell transforms, and explores its properties, uncertainty principles, and applications in time-frequency analysis.

Contribution

It develops the SAST, derives its fundamental properties, establishes uncertainty principles, and links it to the special affine scaled Wigner distribution, with potential applications.

Findings

Derived fundamental properties and inversion formula for SAST

Established uncertainty principles related to SAST

Presented applications with simulation results

Abstract

In this paper, we study the convolution structure in the special affine Fourier transform domain to combine the advantages of the well known special affine Fourier and Stockwell transforms into a novel integral transform coined as special affine Stockwell transform and investigate the associated constant Q property in the joint time frequency domain. The preliminary analysis encompasses the derivation of the fundamental properties, Rayleighs energy theorem, inversion formula and range theorem. Besides, we also derive a direct relationship between the recently introduced special affine scaled Wigner distribution and the proposed SAST. Further, we establish Heisenbergs uncertainty principle, logarithmic uncertainty principle and Nazarovs uncertainty principle associated with the proposed SAST. Towards the culmination of this paper, some potential applications with simulation are presented.