Applications of the fractional Fourier transform in optics and signal processing: a review

Haldun M. Ozaktas

doi:10.1117/12.2299085

1 September 1996 Applications of the fractional Fourier transform in optics and signal processing: a review

Haldun M. Ozaktas

Proceedings Volume 2778, 17th Congress of the International Commission for Optics: Optics for Science and New Technology; 27785M (1996) https://doi.org/10.1117/12.2299085
Event: 17th Congress of the International Commission for Optics: Optics for Science and New Technology, 1996, Taejon, Korea, Republic of

Abstract

The fractional Fourier transform The fractional Fourier transform is a generalization of the common Fourier transform with an order parameter a. Mathematically, the ath order fractional Fourier transform is the ath power of the fractional Fourier transform operator. The a = 1st order fractional transform is the common Fourier transform. The a = 0th transform is the function itself. With the development of the fractional Fourier transform and related concepts, we see that the common frequency domain is merely a special case of a continuum of fractional domains, and arrive at a richer and more general theory of alternate signal representations, all of which are elegantly related to the notion of space-frequency distributions. Every property and application of the common Fourier transform becomes a special case of that for the fractional transform. In every area in which Fourier transforms and frequency domain concepts are used, there exists the potential for generalization and improvement by using the fractional transform.

Citation Download Citation

Haldun M. Ozaktas "Applications of the fractional Fourier transform in optics and signal processing: a review", Proc. SPIE 2778, 17th Congress of the International Commission for Optics: Optics for Science and New Technology, 27785M (1 September 1996); https://doi.org/10.1117/12.2299085

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