On the extension of the coupled fractional Fourier transform and its properties. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Kamalakkannan, R.; Roopkumar, R.; Zayed, A.
• Is Part Of: Integral transforms and special functions. Volume 33:Issue 1(2022)
• Page Start: 65
• Page End: 80
• Publication Date: 2022-01-02
• Subjects: Two-dimensional fractional Fourier transform -- Hermite polynomials of two complex variables -- additive property -- inversion theorem; 42B10 -- 42A38 -- 44A15 -- 44A35; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2021.1902320
• Languages: English
• ISSNs: 1065-2469

Abstract

Abstract : The coupled fractional Fourier transform is a two-dimensional fractional Fourier transform F α, β that depends on two angles α, β that are coupled in such a way that the transform parameters are γ = ( α + β ) / 2 and η = ( α − β ) / 2. It generalizes the two-dimensional Fourier transform and it serves as useful tool in some applications in optics and signal processing. In this article we derive new properties of the transform, such as its additive property. We then extend some of them to L 2 ( R 2 ) and show that the transform is a unitary operator on L 2 ( R 2 ) .