Properties of the fractionalization of a Fourier transform

Shutian Liu; Jingde Zhang; Yan Zhang

doi:10.1016/S0030-4018(96)00478-6

Properties of the fractionalization of a Fourier transform

Shutian Liu^*
, Jingde Zhang
, Yan Zhang

^*Corresponding author for this work

School of Physics

Shenzhen Science Hall
Harbin Institute of Technology

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

30 Scopus citations

Abstract

The new fractional Fourier transform, proposed by Shih [Optics Comm. 118 (1995) 495], is shown to differ from the conventional fractional Fourier transform by its four periodic eigenvalues with respect to the order of Hermite-Gaussian functions. Simulations demonstrate that the Hermite-Gaussian superposition algorithm is still valid for this new transform. We also propose a general fractionalization procedure which includes these two definitions as two limits.

Original language	English
Pages (from-to)	50-54
Number of pages	5
Journal	Optics Communications
Volume	133
Issue number	1-6
DOIs	https://doi.org/10.1016/S0030-4018(96)00478-6
State	Published - 1 Jan 1997

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10.1016/S0030-4018(96)00478-6

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title = "Properties of the fractionalization of a Fourier transform",

abstract = "The new fractional Fourier transform, proposed by Shih [Optics Comm. 118 (1995) 495], is shown to differ from the conventional fractional Fourier transform by its four periodic eigenvalues with respect to the order of Hermite-Gaussian functions. Simulations demonstrate that the Hermite-Gaussian superposition algorithm is still valid for this new transform. We also propose a general fractionalization procedure which includes these two definitions as two limits.",

author = "Shutian Liu and Jingde Zhang and Yan Zhang",

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AU - Zhang, Jingde

AU - Zhang, Yan

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N2 - The new fractional Fourier transform, proposed by Shih [Optics Comm. 118 (1995) 495], is shown to differ from the conventional fractional Fourier transform by its four periodic eigenvalues with respect to the order of Hermite-Gaussian functions. Simulations demonstrate that the Hermite-Gaussian superposition algorithm is still valid for this new transform. We also propose a general fractionalization procedure which includes these two definitions as two limits.

AB - The new fractional Fourier transform, proposed by Shih [Optics Comm. 118 (1995) 495], is shown to differ from the conventional fractional Fourier transform by its four periodic eigenvalues with respect to the order of Hermite-Gaussian functions. Simulations demonstrate that the Hermite-Gaussian superposition algorithm is still valid for this new transform. We also propose a general fractionalization procedure which includes these two definitions as two limits.

UR - https://www.scopus.com/pages/publications/0030736926

U2 - 10.1016/S0030-4018(96)00478-6

DO - 10.1016/S0030-4018(96)00478-6

M3 - 文章

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SN - 0030-4018

VL - 133

SP - 50

EP - 54

JO - Optics Communications

JF - Optics Communications

IS - 1-6

ER -

Properties of the fractionalization of a Fourier transform

Abstract

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