Author:

Keywords:

fractional Fourier transform, Harpers equation, Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, HARPERS EQUATION, 0101 Pure Mathematics, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, Numerical & Computational Mathematics, 4901 Applied mathematics, 4904 Pure mathematics

Abstract:

In this paper we make a critical comparison of some MATLAB programs for the digital computation of the fractional Fourier transform that are freely available and we describe our own implementation that filters the best out of the existing ones. Two types of transforms are considered: first, the fast approximate fractional Fourier transform algorithm for which two algorithms are available. The method is described in [H.M. Ozaktas, M.A. Kutay, G. Bozdagi, IEEE Trans. Signal Process. 44 (1996) 2141-2150]. There are two implementations: one is written by A.M. Kutay, the other is part of package written by J. O'Neill. Second, the discrete fractional Fourier transform algorithm described in the master thesis by C. Candan [Bilkent University, 1998] and an algorithm described by S.C. Pei, M.H. Yeh, and C.C. Tseng [IEEE Trans. Signal Process. 47 (1999) 1335-1348].