Computation of the Fractional Fourier Transform
Computation of the Fractional Fourier Transform
Adhemar Bultheel
Hector Martínez-Sulbaran
Abstract:
In this note we make a critical comparison of some matlab programs for the
digital computation of the fractional Fourier transform that are freely
available.
There is the fast fractional Fourier transform algorithm for which two
algorithms are available. The method is described in
H.M. Ozaktas, M.A. Kutay, and G. Bozdagi.
Digital computation of the fractional Fourier transform.
IEEE Trans. Signal Process., 44:2141--2150, 1996.
There are two implementations: one is written by A.M. Kutay
the other is part of package written by J. O'Neill.
On the other hand there is the discrete fractional Fourier transform algorithm
described in the master thesis
C. Candan.
The discrete fractional Fourier transform,
Bilkent Univ., 1998
and an algorithm described by S.C. Pei, M.H. Yeh, and C.C Tseng:
Digital fractional Fourier transform based on orthogonal projections
IEEE Trans. Signal Process., 47:1335--1348, 1999.
This note discusses some of the implementation aspects.
Status:
Published in Applied and Computational Harmonic Analysis
BiBTeX entry:
@article{ArtBM03a,
author = "A. Bultheel and Mart{\'i}nez-Sulbaran, H.",
title = "Computation of the Fractional {F}ourier Transform",
journal = "Applied and Computational Harmonic Analysis",
year = "2004",
pages = "182-202",
number = "3",
volume = "16",
url = "http://nalag.cs.kuleuven.be/papers/ade/frftcomp/index.html",
DOI = "10.1016/j.acha.2004.02.001",
LIMO = "1128238",
ZBL = "1049.65156",
MR = "2054278",
}
File(s):
preprint.pdf (490K)
For the matlab files described in the text see
here.