Fourier analysis of time series: an introduction
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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The Search for Periodicity
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algorithm aliasing APPFLG applied approximately autocovariances Brillinger coherency complex demodulation computed convergence factors corresponding 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 multiple nonnegative nonzero Note Nyquist frequency observations oscillations output parameters peaks periodogram ordinates REAL ARRAY residuals result RETURN END 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 variable-star data variance Verify wheat-price white-noise zero