A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction with the Wigner distribution of a signal. Convolution, filtering, and multiplexing of signals in fractional domains are discussed, revealing that under certain conditions one can improve on the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing.
© 1994 Optical Society of America
Original Manuscript: June 1, 1993
Manuscript Accepted: August 18, 1993
Published: February 1, 1994
Haldun M. Ozaktas, David Mendlovic, Levent Onural, and Billur Barshan, "Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms," J. Opt. Soc. Am. A 11, 547-559 (1994)