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Chapman and Hall/CRC
519 pages | 206 B/W Illus.
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
Introduction
Definitions
Continuous Sinusoids
Discrete Sinusoids
Harmonic Series
Traveling and Standing Waves
Wave Propagation and Dispersion
Applications of Sinusoids
Historical Notes
Fourier Series
Orthogonality
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
Definitions
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
Noise
Quantization
Digital Signals
Interference
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
Quasi-Optics
Electromagnetic Spectrum
Electromagnetic Radiation
Adaptive Additive Algorithm
X-Ray Crystallography
Historical Notes
Bragg’s Law
X-Ray Diffraction
Generation of X-Rays
DNA
Hydrogen Atom
Units of Measurement
Laser
Radioastronomy
Historical Notes
Synchrotron Radiation
Radioastronomy
Radio Interferometry
Aperture Synthesis
Big Bang, Quasars, and Pulsars
Black Holes
Acoustics, Poetry, and Music
Introduction
Harmonic Analysis
Huygens Principle Revisited
Modulation
Rhythm and Music
Drums
Music Synthesizers
Computerized Axial Tomography
Introduction
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
Bibliography
Index
