## Fourier Analysis of Time Series: An IntroductionThe search for periodicity; Harmonic analysis; The fast fourier transform; Examples of harmonic analysis; Complex demodulation; The spectrum; Some stationary time series theory; Analysis of multiple series; Further topics. |

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### Contents

Introduction | 1 |

The Search for Periodicity | 9 |

Harmonic Analysis | 42 |

Copyright | |

8 other sections not shown

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### Common terms and phrases

algorithm aliasing APPFLG applied approximately autocovariances Brillinger coherency complex demodulation computed convergence factors corresponding covariances cross covariances cross periodogram cross spectrum data window DATIN defined derived described in Section discrete Fourier transform equations errors Exercise exponentially distributed fast Fourier transform Fourier analysis Fourier frequencies Fourier series graph harmonic analysis hence index of fluctuations input integer inverse jointly weakly stationary leakage least squares linear filter logarithms method modified Daniell multiple nonnegative nonzero Note Nyquist frequency observations oscillations output parameters peaks periodogram ordinates REAL ARRAY residuals result second harmonic Section 6.2 sequence series length set of data shown in Figure shows sidelobes simple moving average simplest sinusoid smooth spectral density spectral density function spectral weights spectral window spectrum estimate Statistics stretch of data SUBROUTINE sum of squares sunspot sunspot numbers Suppose symmetric tapered tion transfer function troughs twiddle factor variable-star data variance Verify wheat-price white-noise zero

### References to this book

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