A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform-Reference-Cited by-同舟云学术

A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform

Published:2016 Issue: Volume:2016 Page:1-11
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Bahri Mawardi¹^ORCID,Ashino Ryuichi²^ORCID

Affiliation:

1. Department of Mathematics, Hasanuddin University, Makassar 90245, Indonesia

2. Division of Mathematical Sciences, Osaka Kyoiku University, Osaka 582-8582, Japan

Abstract

We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT) by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT). We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied.

Funder

Hasanuddin University, Indonesia

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2016/5874930.pdf

Reference20 articles.

1. A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics

2. A Tighter Uncertainty Principle for Linear Canonical Transform in Terms of Phase Derivative

3. Uncertainty Principles for Linear Canonical Transform