Sinusoids: Theory and Technological Applications

Content: 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
Abstract: 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