Sinusoids

<p><em>A Complete Treatment of Current Research Topics in Fourier Transforms and Sinusoids </em></p><p></p><p><strong>Sinusoids: Theory and Technological Applications</strong> 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.</p><p></p><p>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.</p>