Continuous vs. discrete fractional Fourier transforms

被引：54

作者：

Atakishiyev, NM

Vicent, LE

Wolf, KB

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

[2] Univ Autonoma Estado Morelos, Fac Ciencias, Mexico City, DF, Mexico

[3] Univ Nacl Autonoma Mexico, Ctr Ciencias Fis, Cuernavaca 62251, Morelos, Mexico

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1999年 / 107卷 / 01期

关键词：

fractional Fourier transform; Kravchuk (Krawtchouk) polynomial; waveguide; coherent state;

D O I：

10.1016/S0377-0427(99)00082-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We compare the finite Fourier (-exponential) and Fourier-Kravchuk transforms; both are discrete, finite versions of the Fourier integral transform. The latter is a canonical transform whose fractionalization is well defined. We examine the harmonic oscillator wavefunctions and their finite counterparts: Mehta's basis functions and the Kravchuk functions. The fractionalized Fourier-Kravchuk transform was proposed in J. Opt. Sec, Amer. A (14 (1997) 1467-1477) and is here subject of numerical analysis. In particular, we follow the harmonic motions of coherent states within a finite, discrete optical model of a shallow multimodal waveguide. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：73 / 95

页数：23

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