Multiplicity of fractional Fourier transforms and their relationships

Author

Cariolaro, Gianfranco ; Erseghe, Tomaso ; Kraniauskas, Peter ; Laurenti, Nicola

Author_Institution

Dipt. di Elettronica e Inf., Padova Univ., Italy

Volume

48

Issue

1

fYear

2000

fDate

1/1/2000 12:00:00 AM

Firstpage

227

Lastpage

241

Abstract

The multiplicity of the fractional Fourier transform (FRT), which is intrinsic in any fractional operator, has been claimed by several authors, but never systematically developed. The paper starts with a general FRT definition, based on eigenfunctions and eigenvalues of the ordinary Fourier transform, which allows us to generate all possible definitions. The multiplicity is due to different choices of both the eigenfunction and the eigenvalue classes. A main result, obtained by a generalized form of the sampling theorem, gives explicit relationships between the different FRTs

Keywords

Fourier transforms; eigenvalues and eigenfunctions; mathematical operators; signal sampling; eigenfunctions; eigenvalues; fractional Fourier transforms; fractional operator; ordinary Fourier transform; sampling theorem; Discrete Fourier transforms; Eigenvalues and eigenfunctions; Fourier transforms; Information processing; Kernel; Multidimensional systems; Optical fibers; Optical signal processing; Sampling methods; Signal sampling;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.815493

Filename

815493