Clifford-valued linear canonical Stockwell transform

TL;DR

This paper introduces a novel Clifford-valued linear canonical Stockwell transform that enhances high-dimensional time-frequency analysis by offering greater directional flexibility and localized windowing, with proven theoretical properties and practical validation.

Contribution

It presents a new Clifford-valued transform that improves signal representation in high-dimensional analysis, incorporating angular and scalable windows for better directional sensitivity.

Findings

The transform satisfies key properties like inner product relation and reconstruction formula.

Practical examples confirm the theoretical results.

Enhances multi-scale signal analysis in the Clifford domain.

Abstract

We present a new Clifford-valued linear canonical Stockwell transform aimed at providing efficient and focused representation of Clifford-valued functions in high-dimensional time-frequency analysis. This transform improves upon the windowed Fourier and wavelet transforms by incorporating angular, scalable, and localized windows, allowing for greater directional flexibility in multi-scale signal analysis within the Clifford domain. Using operator theory, we explore the core properties of the proposed transform, such as the inner product relation, reconstruction formula, and interval theorem. Practical examples are included to confirm the validity of the derived results.