Handbook of Fourier Analysis & Its Applications

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Oxford University Press, Jan 8, 2009 - Technology & Engineering - 800 pages
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Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal processing and related multidimensional transform theory, and quantum physics to elementary deterministic finance and even the foundations of western music theory. As a definitive text on Fourier Analysis, Handbook of Fourier Analysis and Its Applications is meant to replace several less comprehensive volumes on the subject, such as Processing of Multifimensional Signals by Alexandre Smirnov, Modern Sampling Theory by John J. Benedetto and Paulo J.S.G. Ferreira, Vector Space Projections by Henry Stark and Yongyi Yang and Fourier Analysis and Imaging by Ronald N. Bracewell. In addition to being primarily used as a professional handbook, it includes sample problems and their solutions at the end of each section and thus serves as a textbook for advanced undergraduate students and beginning graduate students in courses such as: Multidimensional Signals and Systems, Signal Analysis, Introduction to Shannon Sampling and Interpolation Theory, Random Variables and Stochastic Processes, and Signals and Linear Systems.

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1 Introduction
2 Fundamentals of Fourier Analysis
3 Fourier Analysis in Systems Theory
4 Fourier Transforms in Probability Random Variables and Stochastic Processes
5 The Sampling Theorem
6 Generalizations of the Sampling Theorem
7 Noise and Error Effects
8 Multidimensional Signal Analysis
10 Signal Recovery
Alternating Projections Onto Convex Sets
12 Mathematical Morphology and Fourier Analysis on Time Scales
13 Applications
14 Appendices
15 References

9 TimeFrequency Representations

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About the author (2009)

Robert J. Marks II, Ph.D., is Distinguished Professor of Engineering in the Department of Engineering at Baylor University. He came to Baylor University after 26 years at the University of Washington in Seattle. Robert J. Marks II has eight books (author, co-author, editor or co-editor) published by IEEE, MIT Press and Oxford University Press, three patents, over 50 supervised doctoral dissertations and masters theses, and over 300 publications.

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