From Book News, Inc.
The fractional version is a generalization of the ordinary Fourier transform, and Ozaktas (Bilkent U. Ankara), Zeev Zalevsky (Tel Aviv U.), and M. Alper Kutay (TBBITAK-UEKAE, Ankara) say it is richer in theory and more flexible in applications but not more costly in implementation, and can be an improvement over the garden variety in almost any context where Fourier transforms are used. Primarily for graduate students and researchers in mathematics, science, and engineering, they explain the basic concepts from various perspectives, and survey its application in two areas where it is widely used. Mathematical rigor is left to the references, and the sections on optics are segregated and easily skipped by readers with no background or interest.Copyright © 2004 Book News, Inc., Portland, OR
Review
"...[the authors] explain the basic concepts from various perspectives and survey its application in two areas where it is widely used." (SciTech Book News, Vol. 25, No. 4, December 2001)
"...will surely have a significant impact in those areas of mathematics, science and engineering where Fourier transforms and related concepts are used..." (IEEE Control Systems Magazine, October 2002)
Review
"...[the authors] explain the basic concepts from various perspectives and survey its application in two areas where it is widely used." (SciTech Book News, Vol. 25, No. 4, December 2001)
"...will surely have a significant impact in those areas of mathematics, science and engineering where Fourier transforms and related concepts are used..." (IEEE Control Systems Magazine, October 2002)
Book Description
The discovery of the Fractional Fourier Transform and its role in optics and data management provides an elegant mathematical framework within which to discuss diffraction and other fundamental aspects of optical systems. This book explains how the fractional Fourier transform has allowed the generalization of the Fourier transform and the notion of the frequency transform. It will serve as the standard reference on Fourier transforms for many years to come.
From the Back Cover
The Fractional Fourier Transform provide a comprehensive and widely accessible account of the subject covering both theory and applications. As a generalisation of the Fourier transform, the fractional Fourier transform is richer in theory and more flexible in applications but not more costly in implementation. This text consolidates knowledge on the transform and illustrates its application in diverse contexts. Applications studied so far fall mostly in the areas in optics and wave propagation and signal processing, including optical information processing, beam synthesis, phase retrieval, perspective projections, shift-variant filtering, image restoration, pattern recognition, tomography, data compression and time-frequency representations. Background material introduces time-frequency analysis emphasizing the Wigner distribution, ambiguity function and canonical transforms. Chapter on phase-space optics employs matrix algebra 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. Separate discussion of optics for readers with no interest in optics. Unifying knowledge from the mathematics, optics and signal processing literature in a manner accessible to a broad audience, this book is of interest to researchers, engineers, and senior undergraduate and graduate students in electrical engineering, physics, and mathematics.
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