A unified framework for the fractional Fourier transform

Author

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

Author_Institution

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

Volume

46

Issue

12

fYear

1998

fDate

12/1/1998 12:00:00 AM

Firstpage

3206

Lastpage

3219

Abstract

The paper investigates the possibility for giving a general definition of the fractional Fourier transform (FRT) for all signal classes [one-dimensional (1-D) and multidimensional, continuous and discrete, periodic and aperiodic]. Since the definition is based on the eigenfunctions of the ordinary Fourier transform (FT), the preliminary conditions is that the signal domain/periodicity be the same as the FT domain/periodicity. Within these classes, a general FRT definition is formulated, and the FRT properties are established. In addition, the multiplicity (which is intrinsic in a fractional operator) is clearly developed. The general definition is checked in the case in which the FRT is presently available and, moreover, to establish the FRT in new classes of signals

Keywords

Fourier transforms; eigenvalues and eigenfunctions; signal processing; 1D signals; FT domain/periodicity; Fourier transform; aperiodic signals; continuous signals; discrete signals; eigenfunctions; fractional Fourier transform; fractional operator; general definition; multidimensional signals; periodic signals; signal classes; signal domain/periodicity; Chirp; Eigenvalues and eigenfunctions; Fourier transforms; Helium; Information processing; Multidimensional signal processing; Multidimensional systems; Optical fibers; Optical signal processing; Topology;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.735297

Filename

735297