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Physics - Theoretical, Mathematical & Computational Physics | Digital Fourier Analysis

Digital Fourier Analysis

Kido, Ken'iti

2014, XXVI, 381 p. 2 volume-set.

Softcover
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ISBN 978-1-4939-1521-7

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Due: October 14, 2014


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  • Covers the basic theory of the discrete and Fast Fourier transform and shows how they are implemented, using clear explanations and a large number of step-by-step illustrations
  • Interactive animated applets, freely available online, richly illustrate the book and allow the reader to explore the subject dynamically
  • Practice problems are included at the end of each chapter
  • A large number of Appendices provide more detailed derivations and explanations for the interested reader
This set collects the fundamental and advanced techniques outlined in both volumes. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. The second volume covers advanced topics including the Hilbert transform, cepstrum analysis, and the two-dimensional Fourier transform. Saturated with clear, coherent illustrations, Digital Fourier Analysis includes practice problems and thorough Appendices for the advanced reader. As a special feature, interactive applets (available online) that mirror the illustrations are included. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader can test various cases and view the results until they fully understand the principle. Additionally, the applet source code in Visual Basic is provided online, allowing this book to be used for teaching simple programming techniques. A complete, intuitive guide, Digital Fourier Analysis is an essential reference for undergraduate and graduate students in science and engineering.

Content Level » Upper undergraduate

Related subjects » Analysis - Computational Intelligence and Complexity - Theoretical, Mathematical & Computational Physics - Theoretical Computer Science

Table of contents 

Book 1.- Preface.- Sine and Cosine Waves.- Fourier Series Expansion.- Numerical (sampled) Waveforms.- Discrete Fourier transform (DFT).- Fast Fourier transform (FFT).- DFT and spectrum.- Time window.- Appendices.- Book 2.- Convolution.- Correlation function.- Cross-spectrum method.- Cepstrum analysis.- Hilbert transform.- 2-D transform.- Appendices.

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