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.
By:
Prem K. Kythe
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Dimensions:
Height: 234mm,
Width: 156mm,
Spine: 33mm
Weight: 861g
ISBN: 9781482221060
ISBN 10: 1482221063
Pages: 519
Publication Date: 08 July 2014
Audience:
College/higher education
,
College/higher education
,
A / AS level
,
Further / Higher Education
Format: Hardback
Publisher's Status: Active
Introduction. Fourier Series. Fourier Transforms. Signals and Filters. Communication Systems. Global Positioning System. Fourier Optics. X-Ray Crystallography. Radioastronomy. Acoustics, Poetry, and Music. Computerized Axial Tomography. Appendices. Bibliography. Index.
Prem K. Kythe is a Professor Emeritus of Mathematics at the University of New Orleans. He is the author/coauthor of ten books and author of 46 research papers. His research interests encompass the fields of complex analysis, continuum mechanics, and wave theory, including boundary element methods, finite element methods, conformal mappings, PDEs and boundary value problems, linear integral equations, computation integration, fundamental solutions of differential operators, Green’s functions, and coding theory.
Reviews for Sinusoids: Theory and Technological Applications
"""... 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"
