A Version of Uncertainty Principle for Quaternion Linear Canonical Transform

Mawardi Bahri,Selvy Musdalifah,Resnawati Resnawati

doi:10.1155/2018/8732457

Mawardi Bahri, Selvy Musdalifah + Show 1 more

Open Access

https://doi.org/10.1155/2018/8732457

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Abstract

In recent years, the two-dimensional (2D) quaternion Fourier and quaternion linear canonical transforms have been the focus of many research papers. In the present paper, based on the relationship between the quaternion Fourier transform (QFT) and the quaternion linear canonical transform (QLCT), we derive a version of the uncertainty principle associated with the QLCT. We also discuss the generalization of the Hausdorff-Young inequality in the QLCT domain.

Highlights

The quaternion Fourier transform (QFT) is an extension of the classical two-dimensional Fourier transform (FT) [1,2,3,4] in the framework of quaternion algebra
In the present paper, based on the relationship between the quaternion Fourier transform (QFT) and the quaternion linear canonical transform (QLCT), we derive a version of the uncertainty principle associated with the QLCT
The right-sided quaternion linear canonical transform is obtained by substituting the Fourier kernel with the right-sided QFT kernel in the LCT definition, and so on

Summary

A Version of Uncertainty Principle for Quaternion Linear Canonical Transform

Received 2 October 2017; Revised 18 March 2018; Accepted 2 April 2018; Published 7 May 2018. The two-dimensional (2D) quaternion Fourier and quaternion linear canonical transforms have been the focus of many research papers. In the present paper, based on the relationship between the quaternion Fourier transform (QFT) and the quaternion linear canonical transform (QLCT), we derive a version of the uncertainty principle associated with the QLCT. We discuss the generalization of the Hausdorff-Young inequality in the QLCT domain

Introduction

Preliminaries

A Version of Uncertainty Principle Associated with QLCT

Conclusion