Discrete quadratic-phase Fourier transform: Theory and convolution structures

Date

2022

Authors

Srivastava, H.M.
Lone, Waseem Z.
Shah, Firdous A.
Zayed, Ahmed I.

Journal Title

Journal ISSN

Volume Title

Publisher

Entropy

Abstract

The discrete Fourier transform is considered as one of the most powerful tools in digital signal processing, which enable us to find the spectrum of finite-duration signals. In this article, we introduce the notion of discrete quadratic-phase Fourier transform, which encompasses a wider class of discrete Fourier transforms, including classical discrete Fourier transform, discrete fractional Fourier transform, discrete linear canonical transform, discrete Fresnal transform, and so on. To begin with, we examine the fundamental aspects of the discrete quadratic-phase Fourier transform, including the formulation of Parseval’s and reconstruction formulae. To extend the scope of the present study, we establish weighted and non-weighted convolution and correlation structures associated with the discrete quadratic-phase Fourier transform.

Description

Keywords

quadratic-phase Fourier transform, discrete quadratic-phase Fourier transform, convolution

Citation

Srivastava, H. M., Lone, W. Z., Shah, F. A., & Zayed, A. I. (2022). “Discrete quadratic-phase Fourier transform: Theory and convolution structures.” Entropy, 24(10), 1340. https://doi.org/10.3390/e24101340