Convolution, filtering, and multiplexing in fractional fourier domains and their relation to chirp and wavelet transforms

Haldun M. Ozaktas, Billur Barshan, David Mendlovic, Lèvent Onural

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)547-559
Number of pages13
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume11
Issue number2
DOIs
StatePublished - Feb 1994

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