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Journal of Physics Conference Series

Two Uncertainty Principles Related to the Linear Canonical S-Transform

Mawardi Bahri

Published Oct 1, 2019• 1 citation
Publisher

Abstract

Abstract In this article we derive uncertainty principles for the linear canonical S-transform. This uncertainty principles are obtained by applying the properties and relation between the linear canonical transform and the linear canonical S-transform.
DOI
10.1088/1742-6596/1341/6/062006

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The linear canonical transform (LCT) is the name of a parameterized continuum of transforms that include, as particular cases, many widely used transforms in optics such as the Fourier transform, fractional Fourier transform, and Fresnel transform. It provides a generalized mathematical tool for representing the response of any first-order optical system in a simple and insightful way. In this work we present four uncertainty relations between LCT pairs and discuss their implications in some common optical systems.
Some properties of the qqq-Fourier-sine transform are studied and qqq-analogues of the Heisenberg uncertainty principle is derived for the qqq-Fourier-cosine transform studied in \cite{FB} and for the qqq-Fourier-sine transform.