## Fractional finite Fourier transform

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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### References

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