Sinusoids
Subtitle: theory and technological applications
By: Prem K. Kythe, University of New Orleans, Louisiana, USA
Series: Monographs and research notes in mathematics; Monographs and research notes in mathematics
Publisher: CRC Press; Taylor & Francis Group
Published: 2015
Place of publication: Boca Raton; London
Language: eng
Number of pages: 487
ISBN-13: 9781482221060
Subjects: Fourier transformations; Fourier transform optics; Signal processing
Description: 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. He 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.--
Notes: "A Chapman & Hall book."

Includes bibliographical references (pages 463-477) and index.
Table of contents: title: 1. Introduction; title: 2. Fourier series; title: 3. Fourier transforms; title: 4. Signals and filters; title: 5. Communication systems; title: 6. Global positioning system; title: 7. Fourier optics; title: 8. X-ray crystallography; title: 9. Radioastronomy; title: 10. Acoustics, poetry, and music; title: 11. Computerized axial tomography.