Wigner distribution moments measured as intensity moments in the fractional Fourier transform domain

Martin J. Bastiaans and Tatiana Alieva

Technische Universiteit Eindhoven, Faculteit Elektrotechniek
Postbus 513, 5600 MB Eindhoven, Netherlands

We show how all global Wigner distribution moments of arbitrary order can be measured as intensity moments in the output plane of an appropriate number of fractional Fourier transform systems (generally anamorphic ones), and we derive the minimum number of (anamorphic) fractional power spectra that are needed for the determination of these moments. The results follow directly from the general relationship that expresses the intensity moments in the output plane of an anamorphic fractional Fourier transform system in terms of the moments in the input plane and the two angles. They can also be derived by formulating rotation-type input-output-relationships between certain combinations of moments. The latter method yields, as a by-product, a number of moment combinations that are invariant under anamorphic fractional Fourier transformation.

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