Fourier Analysis of Time Series: An Introduction (Google eBook)

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John Wiley & Sons, Apr 5, 2004 - Mathematics - 288 pages
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A new, revised edition of a yet unrivaled work on frequency domain analysis

Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample exercises acquaint readers with Fourier analysis and its applications. The Second Edition:

  • Devotes an entire chapter to complex demodulation
  • Treats harmonic regression in two separate chapters
  • Features a more succinct discussion of the fast Fourier transform
  • Uses S-PLUS commands (replacing FORTRAN) to accommodate programming needs and graphic flexibility
  • Includes Web addresses for all time series data used in the examples

An invaluable reference for statisticians seeking to expand their understanding of frequency domain methods, Fourier Analysis of Time Series, Second Edition also provides easy access to sophisticated statistical tools for scientists and professionals in such areas as atmospheric science, oceanography, climatology, and biology.

  

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Contents

1 Introduction
1
2 Fitting Sinusoids
9
3 The Search for Periodicity
25
4 Harmonic Analysis
37
5 The Fast Fourier Transform
57
6 Examples of Harmonic Analysis
63
7 Complex Demodulation
97
8 The Spectrum
133
9 Some Stationary Time Series Theory
167
10 Analysis of Multiple Series
201
11 Further Topics
233
References
247
Author Index
255
Subject Index
257
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About the author (2004)

PETER BLOOMFIELD, PhD, is a professor in the Department of Statistics at North Carolina State University, Raleigh.