## Fourier Analysis of Time Series: An IntroductionA 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

Introduction | 1 |

The Search for Periodicity | 9 |

The Fast Fourier Transform | 61 |

Copyright | |

2 other sections not shown

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### Common terms and phrases

algorithm amplitude analysis applied approximately average CALL Chapter close coefficients coherency complex components computed consider consists constant contains continuous corresponding cosine cross defined demodulation depend derived described discrete discussed distribution effect equations errors example Exercise extended fact factor Figure filter fluctuations follows Fourier frequencies Fourier transform give given graph hence independent instance integer interval leakage least squares length linear logarithms mean method moving average multiple normal Note observations obtain original oscillations parameters peaks periodic periodogram phase present problem procedure properties range REAL relatively respectively result RETURN Section sequence shown shows similar simple sinusoid smooth spectral spectrum estimate Statistics sunspot Suppose tapered Theory tion transfer function usually values variable variance weights window zero Х Х

### References to this book

Time Series Analysis and Its Applications Robert H. Shumway,David S. Stoffer No preview available - 2000 |