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The Special Affine Fourier Transform (SAFT) represents the most general lossless inhomogeneous linear mapping in phase space, as an integral transformation of the wavefunction. In this report an overview of recent work relating to the area of linear transformations and optical signal processing is presented. In particular the relationship between the SAFT and the Fractional Fourier Transform (FRT) is examined. In order to fully appreciate these transformations the use of the Wigner Distribution Function (WDF) is reviewed. The Abelian subgroups of the SAFT are also discussed and several potentially useful new transformations are introduced. Application of the resulting ideas in the areas of imaging and signal processing are illustrated.

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Authors: ABE S, Nihon University, College of Science and Technology, Chiba (JP);SHERIDAN J T, JRC Ispra (IT);COUTSOMITROS C T, JRC Ispra (IT);LUCIA A, JRC Ispra (IT)
Bibliographic Reference: EUR 16316 EN (1995) 39pp., FS
Availability: Available from the Public Relations and Publications Unit, JRC Ispra, I-21020 Ispra (IT)
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