Open Access

The Fractional Fourier Transform and Its Application to Energy Localization Problems

EURASIP Journal on Advances in Signal Processing20032003:246759

DOI: 10.1155/S1110865703305086

Received: 20 March 2002

Published: 20 November 2003

Abstract

Applying the fractional Fourier transform (FRFT) and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the -dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. In this paper, we show how this representation formula can be used to solve certain energy localization problems in phase space. Examples of such problems are given by means of some classical results. Although the results on localization problems are classical, the application of generalized Fourier transform enlarges the class of problems that can be solved with traditional techniques.

Keywords

fractional Fourier transform Wigner distribution symplectic transformation energy localization

Authors’ Affiliations

(1)
Department of Nautical Sciences, Royal Netherlands Naval College (KIM)
(2)
Department of Mathematics and Computer Science, Eindhoven University of Technology

Copyright

© Copyright © 2003 Hindawi Publishing Corporation 2003