Generalized fractional Fourier transforms

Shutian Liu; Jiuxing Jiang; Yan Zhang; Jingde Zhang

doi:10.1088/0305-4470/30/3/020

Generalized fractional Fourier transforms

Shutian Liu^*
, Jiuxing Jiang
, Yan Zhang
, Jingde Zhang

^*Corresponding author for this work

School of Physics

Harbin University of Science and Technology
Harbin Institute of Technology
Shenzhen Science Hall

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We generalize the definition of the fractional Fourier transform (FRT) by expanding the new definition proposed by Shih to the original definition. The generalized FRT is shown to have k-periodic eigenvalues with respect to the order of Hermite-Gaussian functions and will be reduced to the original FRT and Shih's FRT at the two limits with k = ∞ and k = 4, respectively. The results of computer simulations and symbolic representations of the transform are given. Properties of the generalized FRT have been discussed.

Original language	English
Pages (from-to)	973-981
Number of pages	9
Journal	Journal of Physics A: Mathematical and General
Volume	30
Issue number	3
DOIs	https://doi.org/10.1088/0305-4470/30/3/020
State	Published - 7 Feb 1997

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title = "Generalized fractional Fourier transforms",

abstract = "We generalize the definition of the fractional Fourier transform (FRT) by expanding the new definition proposed by Shih to the original definition. The generalized FRT is shown to have k-periodic eigenvalues with respect to the order of Hermite-Gaussian functions and will be reduced to the original FRT and Shih's FRT at the two limits with k = ∞ and k = 4, respectively. The results of computer simulations and symbolic representations of the transform are given. Properties of the generalized FRT have been discussed.",

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T1 - Generalized fractional Fourier transforms

AU - Liu, Shutian

AU - Jiang, Jiuxing

AU - Zhang, Yan

AU - Zhang, Jingde

PY - 1997/2/7

Y1 - 1997/2/7

N2 - We generalize the definition of the fractional Fourier transform (FRT) by expanding the new definition proposed by Shih to the original definition. The generalized FRT is shown to have k-periodic eigenvalues with respect to the order of Hermite-Gaussian functions and will be reduced to the original FRT and Shih's FRT at the two limits with k = ∞ and k = 4, respectively. The results of computer simulations and symbolic representations of the transform are given. Properties of the generalized FRT have been discussed.

AB - We generalize the definition of the fractional Fourier transform (FRT) by expanding the new definition proposed by Shih to the original definition. The generalized FRT is shown to have k-periodic eigenvalues with respect to the order of Hermite-Gaussian functions and will be reduced to the original FRT and Shih's FRT at the two limits with k = ∞ and k = 4, respectively. The results of computer simulations and symbolic representations of the transform are given. Properties of the generalized FRT have been discussed.

UR - https://www.scopus.com/pages/publications/0031557033

U2 - 10.1088/0305-4470/30/3/020

DO - 10.1088/0305-4470/30/3/020

M3 - 文章

AN - SCOPUS:0031557033

SN - 0305-4470

VL - 30

SP - 973

EP - 981

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 3

ER -

Generalized fractional Fourier transforms

Abstract

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