Biquaternion Windowed Linear Canonical Transform
Owais Ahmad, Aijaz Ahmad Dar
TL;DR
This paper introduces the Biquaternion Windowed Linear Canonical Transform (BiQWLCT), establishing its fundamental properties, deriving an uncertainty principle, and demonstrating potential applications in signal analysis.
Contribution
The paper presents the first formulation of BiQWLCT, extending linear canonical transforms to the biquaternion domain with comprehensive theoretical properties.
Findings
BiQWLCT satisfies linearity, shift, and parity properties.
An inversion formula and orthogonality relations are established.
Heisenberg uncertainty principle is derived for BiQWLCT.
Abstract
In this paper, we introduce the notion of windowed linear canonical transform in biquaternion setting namely Biquaternion Windowed Linear Canonical Transform (BiQWLCT) and various properties of BiQWLCT, such as linearity, shift, parity, orthogonality relation, inversion formula, Plancherel theorem are established. Heisenberg uncertainty principle associated with the Biquaternion Windowed Linear Canonical Transform is also derived. Towards the culmination, an example and some potential applications are presented.
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Taxonomy
TopicsControl Systems and Identification · Digital Filter Design and Implementation