[OPTICAL REVIEW Vol. 1, No. 1 (1994) 15-16]

Convolution and Filtering in Fractional Fourier Domains

Haldun M. OZAKTAS,1 Billur BARSHAN1 and David MENDLOVIC2

1Electrical Engineering Department, Bilkent University, 06533 Bilkent, Ankara, Turkey, 2Faculty of Engineering, Tel-Aviv University, 69978 Tel-Aviv, Israel

(Accepted July 1, 1994)

Fractional Fourier transforms, which are related to chirp and wavelet transforms, lead to the notion of fractional Fourier domains. The concept of filtering of signals in fractional domains is developed, revealing that under certain conditions one can improve upon 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.

Key words : optical information processing, Fourier optics, fractional Fourier transforms, spatial filtering



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