## Self-Fourier functions and self-Fourier operators

JOSA A, Vol. 23, Issue 4, pp. 829-834 (2006)

http://dx.doi.org/10.1364/JOSAA.23.000829

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### Abstract

The concept of self-Fourier functions, i.e., functions that equal their Fourier transform, is almost always associated with specific functions, the most well known being the Gaussian and the Dirac delta comb. We show that there exists an infinite number of distinct families of these functions, and we provide an algorithm for both generating and characterizing their distinct classes. This formalism allows us to show the existence of these families of functions without actually evaluating any Fourier or other transform-type integrals, a task often challenging and frequently not even possible.

© 2006 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(000.3870) General : Mathematics

(070.2590) Fourier optics and signal processing : ABCD transforms

**ToC Category:**

Fourier Optics and Optical Signal Processing

**History**

Original Manuscript: August 11, 2005

Revised Manuscript: October 12, 2005

Manuscript Accepted: November 4, 2005

**Citation**

Theodoros P. Horikis and Matthew S. McCallum, "Self-Fourier functions and self-Fourier operators," J. Opt. Soc. Am. A **23**, 829-834 (2006)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-4-829

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