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The Special Affine Fourier Transform (SAFT) represents the most general inhomogeneous linear mapping in phase space, as an integral transformation of a wavefunction. In this monograph 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 appreciate fully 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.

Additional information

Authors: ABE S, Nihon University, College of Science and Technology, Narashinodae (JP);SHERIDAN J T, JRC Ispra (IT)
Bibliographic Reference: Article: Focus on Modern Microscopy (1995)
Record Number: 199511318 / Last updated on: 1995-10-31
Original language: en
Available languages: en