The Fractional Fourier Transform: with Applications in Optics and Signal Processing

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Summary: The aspects of signals and systems in Fractional domains
Review: From my point of view as a deeply intested reader of the book, this book is an excellent source book for those who want to increase his/her knowledge on concepts of signals and sytems. It is a comprehensive study on the signal and system representation in generalized frequency domains with very useful applications in different era of electrical engineering. Starting with a general representation theory and then focusing on time-frequency representations, the book prepares the reader for the novel generalized Fourier trasnform. In this new world, the traditional frequency domain is no more than a special condition. Thus, in any application that Fourier transform can be used, the FrFT lends itself to a variety of applications including image restoration, denoising, optical wave propogation, filtering, quantum mechanics, information theory etc., generally as an optimization problem over a contiuum of frequency domains. You should read this book if you are a EE. Thanks to the authors.

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Summary: I am smarter now
Review: I am an optical engineering student and felt that this book was quite understandable (although I read the optics back half first, which then motivated the mathematical front half for me). It gave me additional insight into the Fourier transform as well as the applications of Fourier analysis in optics. I also learned as much on optics from this book as I have from any dedicated optics book. It has so many jewels that other books don't have that I wish I was rich enough to own a copy rather than having to check it out from the library.

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Summary: The Fractional Fourier Transform
Review: The Fractional Fourier Transform with Applications in Optics and Signal Processing

1. Introduction 2. Signals, Systems, and Transformations 3. Wigner Distributions and Linear Canonical Transforms 4. The Fractional Fourier Transform 5. Time-Order and Space-Order Representations 6. The Discrete Fractional Fourier Transform 7. Optical Signals and Systems 8. Phase-Space Optics 9. The Fractional Fourier Transform in Optics 10. Applications to Filtering, Estimation, and Signal Recovery 11. Applications to Matched Filtering, Detection, and Pattern Recognition

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. [...]

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Summary: Excellent reference on Fractional Fourier Transforms
Review: This is a delightful reference book on the Fractional Fourier Transform. The authors did a great job explaining systems theory leading up to a thorough treatment of the Fractional Fourier Transform and other fractional transforms. Plenty of references are cited leading the reader to a rich source of background and follow-up material. Later chapters delve into suggested applications which complete a rather pleasing read of the entire subject. Buy this book.