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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 21, Iss. 7 — Jul. 1, 2004
  • pp: 1179–1185

Fractional finite Fourier transform

Kedar Khare and Nicholas George  »View Author Affiliations


JOSA A, Vol. 21, Issue 7, pp. 1179-1185 (2004)
http://dx.doi.org/10.1364/JOSAA.21.001179


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Abstract

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias’s definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

© 2004 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(070.2590) Fourier optics and signal processing : ABCD transforms
(200.3050) Optics in computing : Information processing

History
Original Manuscript: November 17, 2003
Revised Manuscript: February 19, 2004
Manuscript Accepted: February 19, 2004
Published: July 1, 2004

Citation
Kedar Khare and Nicholas George, "Fractional finite Fourier transform," J. Opt. Soc. Am. A 21, 1179-1185 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-7-1179

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