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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Sinusoids. Chapman & Hall 2014 (OCoLC)866935389 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Prem K Kythe |

ISBN: | 9781482221077 1482221071 |

OCLC Number: | 883076120 |

Notes: | "A Chapman & Hall book." |

Description: | 1 online resource (xxxii, 487 pages) : illustrations. |

Contents: | 1. Introduction -- 2. Fourier series -- 3. Fourier transforms -- 4. Signals and filters -- 5. Communication systems -- 6. Global positioning system -- 7. Fourier optics -- 8. X-ray crystallography -- 9. Radioastronomy -- 10. Acoustics, poetry, and music -- 11. Computerized axial tomography. |

Series Title: | Monographs and research notes in mathematics. |

Responsibility: | Prem K. Kythe, University of New Orleans, Louisiana, USA. |

### 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.

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"... 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

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