Sinusoids: Theory and Technological Applications, 1st Edition (Hardback) book cover


Theory and Technological Applications, 1st Edition

By Prem K. Kythe

Chapman and Hall/CRC

519 pages | 206 B/W Illus.

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pub: 2014-07-08
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A Complete Treatment of Current Research Topics in Fourier Transforms and Sinusoids

Sinusoids: Theory and Technological Applications explains how sinusoids and Fourier transforms are used in a variety of application areas, including signal processing, GPS, optics, x-ray crystallography, radioastronomy, poetry and music as sound waves, and the medical sciences. With more than 200 illustrations, the book discusses electromagnetic force and sychrotron radiation comprising all kinds of waves, including gamma rays, x-rays, UV rays, visible light rays, infrared, microwaves, and radio waves. It also covers topics of common interest, such as quasars, pulsars, the Big Bang theory, Olbers’ paradox, black holes, Mars mission, and SETI.

The book begins by describing sinusoids—which are periodic sine or cosine functions—using well-known examples from wave theory, including traveling and standing waves, continuous musical rhythms, and the human liver. It next discusses the Fourier series and transform in both continuous and discrete cases and analyzes the Dirichlet kernel and Gibbs phenomenon. The author shows how invertibility and periodicity of Fourier transforms are used in the development of signals and filters, addresses the general concept of communication systems, and explains the functioning of a GPS receiver. The author then covers the theory of Fourier optics, synchrotron light and x-ray diffraction, the mathematics of radioastronomy, and mathematical structures in poetry and music. The book concludes with a focus on tomography, exploring different types of procedures and modern advances. The appendices make the book as self-contained as possible.


"… I highly recommend this book as a good source for individual studies for graduate students, scientists and technical experts."

--Krzysztof Stempak (Wroclaw), Zentralblatt MATH 1306 | 1

Table of Contents



Continuous Sinusoids

Discrete Sinusoids

Harmonic Series

Traveling and Standing Waves

Wave Propagation and Dispersion

Applications of Sinusoids

Historical Notes

Fourier Series


Completeness and Uniform Convergence

Fourier Series

Dirac Delta Function

Delta Function and Dirichlet Kernel

Gibbs Phenomenon

Square Waveform

Examples of Fourier Series

Complex Fourier Coefficients

Fourier Transforms


Finite Fourier Transforms

Fourier Transforms of Two Variables

Fourier Transforms: Discrete Case

Fast Fourier Transform

Multiple Fourier Transform

Fourier Slice Theorem

Signals and Filters

Description of Signals

Convolution and Signals

Theory of Signals

Random Signals

Discrete Fourier Analysis

Fourier Resynthesis: Discrete Case

Theory of Filters

Communication Systems

Communication Channels



Digital Signals


Nonlinear Systems

SDR System

Data Transmission

Space Exploration

Mars Project and Beyond

Global Positioning System

GPS Structure

CDMA Principle

C/A Code Architecture

P Code Architecture

Computational Aspects

Fourier Optics

Physical Optics

Scalar Diffraction Theory


Electromagnetic Spectrum

Electromagnetic Radiation

Adaptive Additive Algorithm

X-Ray Crystallography

Historical Notes

Bragg’s Law

X-Ray Diffraction

Generation of X-Rays


Hydrogen Atom

Units of Measurement



Historical Notes

Synchrotron Radiation


Radio Interferometry

Aperture Synthesis

Big Bang, Quasars, and Pulsars

Black Holes

Acoustics, Poetry, and Music


Harmonic Analysis

Huygens Principle Revisited


Rhythm and Music


Music Synthesizers

Computerized Axial Tomography


Types of Tomography

Magnetic Resonance Imaging

Modern Tomography

Appendix A: Tables of Fourier Transforms

Appendix B: Hilbert Transforms

Appendix C: Radon Transforms

Appendix D: Maxwell’s Equations and Solitons

Appendix E: Modulation

Appendix F: Boolean and Bitwise Operations

Appendix G: Galois Field

Appendix H: GPS Geometry

Appendix I: Gold Codes

Appendix J: Doppler Effect

Appendix K: Bessel Functions

Appendix: Heisenberg’s Uncertainty Principle

Appendix M: Classical Latin Prosody



About the Author

Prem K. Kythe is a Professor Emeritus of Mathematics at the University of New Orleans. He is the author/coauthor of ten books and author of 46 research papers. His research interests encompass the fields of complex analysis, continuum mechanics, and wave theory, including boundary element methods, finite element methods, conformal mappings, PDEs and boundary value problems, linear integral equations, computation integration, fundamental solutions of differential operators, Green’s functions, and coding theory.

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Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Functional Analysis