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
Fourier Optics and Optical Signal Processing
Original Manuscript: August 11, 2005
Revised Manuscript: October 12, 2005
Manuscript Accepted: November 4, 2005
Theodoros P. Horikis and Matthew S. McCallum, "Self-Fourier functions and self-Fourier operators," J. Opt. Soc. Am. A 23, 829-834 (2006)