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The Fractional Fourier Transform
With Applications in Optics and Signal Processing
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Haldun M. Ozaktas, Bilkent University, Ankara, Turkey, M. Alper Kutay,
Drexel University, Philadelphia, USA, and Zeev Zalevsky, Tel-Aviv University, Tel-Aviv, Israel
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0471 96346 1
January 2001
Hardback
532pp
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As a generalization of the Fourier transform, the fractional Fourier transform
is only richer in theory and more flexible in applications - but not more costly in implementation.
Wherever Fourier transforms are used, there exists the potential for generalization and improvement by
using the fractional transform. This book provides a comprehensive and widely accessible account of the
transform covering both theory and applications.
So far applications have been studied mostly in the areas of optics and wave propagation, and signal processing;
some of these are optical information processing, beam synthesis, phase retrieval, perspective projections,
shift-variant filtering, image restoration, pattern recognition, tomography, data compression, and time-frequency
representations. By consolidating knowledge on the transform and illustrating its application in diverse contexts,
the book aims to make possible the discovery of new applications in other areas as well.
The background material includes an introduction to time-frequency analysis emphasizing the Wigner distribution,
ambiguity function, and canonical transforms. The chapters on optics complement texts on Fourier optics, dealing
with optical systems in phase space in terms of canonical transforms. Matrix algebra is employed in a unified
manner for both wave and geometrical optics, leading to many important results, such as those on general Fourier
transform planes and optical invariants.
- Unifies knowledge from the mathematics, optics, and signal processing literature in a manner accessible to a broad audience.
- Discussion of optics completely segregated for readers with no interest or background in optics.
Ozaktas is the recipient of the 1998 ICO International Prize in Optics (jointly with D. Mendlovic) and the 1999
Scientific and Technical Research Council of Turkey Science Award for his contributions to the subject.
Contents:
- Introduction
- Signals, Systems, and Transformations
- Wigner Distributions and Linear Canonical Transforms
- The Fractional Fourier Transform
- Time-Order and Space-Order Representations
- The Discrete Fractional Fourier Transform
- Optical Signals and Systems
- Phase-Space Optics
- The Fractional Fourier Transform in Optics
- Applications to Filtering, Estimation, and Signal Recovery
- Applications to Matched Filtering, Detection, and Pattern Recognition
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