文档介绍：THE DISCRETE FRACTIONAL FOURIER TRANSFORM
C¸agatay˜ Candan, M. Alper Kutay, and Haldun M. Ozaktas
Department of Electrical Engineering, Bilkent University, TR-06533, Ankara, Turkey
ABSTRACT the discrete FRT in terms of a particular set of eigenvectors (previ-
ously discussed in [14]) which they claim to be the discrete analogs
We propose and consolidate a definition of the discrete fractional of the Hermite-Gaussian functions. They justify their claims by
Fourier transform which generalizes the discrete Fourier transform numerical observations and simulations. In the present paper we
(DFT) in the same sense that the continuous fractional Fourier provide an analytical development of Pei’s claims with the aim of
transform (FRT) generalizes the continuous ordinary Fourier Trans- consolidating the definition of the discrete FRT.
form. This definition is based on a particular set of eigenvectors
of the DFT which constitutes the discrete counterpart of the set of 2. PRELIMINARIES
Hermite-Gaussian functions. The fact that this definition satisfies
all the desirable properties expected of the discrete FRT, supports . Continuous Fractional Fourier Transform
our confidence that it will be accepted as the definitive definition The continuous FRT can be defined through its integral kernel:
of this transform.
Z
1
a
fF f g t =
K t ;t f t dt
a
a
1. INTR