Non-ideal sampling in shift-invariant spaces associated with quadratic-phase Fourier transforms

Lone, Waseem Z.; Shah, Firdous A.; Nisar, Kottakkaran Sooppy; Albalawi, Wedad; Alshahrani, B.; Park, Choonkil

doi:10.1016/j.aej.2022.07.065

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2023

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Cited by 2 publications

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“…For the first time, Srivastava et al discretized the QPFT in 2022 [8]. Following the introduction of the discrete quadratic phase Fourier transform (DQPFT), which is an extension of the discrete Fourier transform (DFT), the applications of the QPFT grow exponentially(see references [9]- [12] ).…”

Section: Introductionmentioning

confidence: 99%

Generalized wave packet transform based on convolution operator in the quaternion quadratic-phase Fourier domain

Dar

Bhat

Rahman

2023

Optik

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Section: Introductionmentioning

confidence: 99%

Generalized wave packet transform based on convolution operator in the quaternion quadratic-phase Fourier domain

Dar

Bhat

Rahman

2023

Optik

View full text Add to dashboard Cite

“…It is worthwhile to mention that QPFT circumscribes several integral transforms, including the classical Fourier, fractional Fourier, Fresnel, linear canonical, and special affine Fourier transforms [ 3 ]. As a generalization of the celebrated Fourier transform, the quadratic-phase Fourier transform gained its ground intermittently and profoundly influenced several disciplines of science and engineering, including harmonic analysis, quantum mechanics, differential equations, optics, pattern recognition, and so on [ 4 , 5 , 6 , 7 ].…”

Section: Introductionmentioning

confidence: 99%

Discrete Quadratic-Phase Fourier Transform: Theory and Convolution Structures

Srivástava

Lone

Shah

et al. 2022

Entropy

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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.

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Non-ideal sampling in shift-invariant spaces associated with quadratic-phase Fourier transforms

Cited by 2 publications

References 10 publications

Generalized wave packet transform based on convolution operator in the quaternion quadratic-phase Fourier domain

Generalized wave packet transform based on convolution operator in the quaternion quadratic-phase Fourier domain

Discrete Quadratic-Phase Fourier Transform: Theory and Convolution Structures

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