Convolution, Correlation and Uncertainty Principle in the One-Dimensional Quaternion Quadratic-Phase Fourier Transform Domain

Mohammad Younus Bhat (), Aamir H. Dar, Mohra Zayed and Altaf A. Bhat
Additional contact information
Mohammad Younus Bhat: Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India
Aamir H. Dar: Department of Mathematical Sciences, Islamic University of Science and Technology, Kashmir 192122, India
Mohra Zayed: Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Altaf A. Bhat: University of Technology and Applied Sciences, Salalah 324, Oman

Mathematics, 2023, vol. 11, issue 13, 1-14

Abstract: In this paper, we present a novel integral transform known as the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT). We first define the one-dimensional quaternion quadratic-phase Fourier transform (1D-QQPFT) of integrable (and square integrable) functions on R . Later on, we show that 1D-QQPFT satisfies all the respective properties such as inversion formula, linearity, Moyal’s formula, convolution theorem, correlation theorem and uncertainty principle. Moreover, we use the proposed transform to obtain an inversion formula for two-dimensional quaternion quadratic-phase Fourier transform. Finally, we highlight our paper with some possible applications.

Keywords: quadratic-phase Fourier transform; quaternion quadratic-phase Fourier transform; convolution; two-dimensional inversion formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/13/3002/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/13/3002/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:13:p:3002-:d:1187655

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().