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.