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Fourier Analysis of Time Series An Introduction

ISBN-10: 0471889482

ISBN-13: 9780471889489

Edition: 2nd 2000 (Revised)

Authors: Peter Bloomfield

List price: $185.00
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Description:

Combining both the theory and the applications of Fourier analysis, this study discusses several topics, including harmonic regression, harmonic analysis, complex demodulation and spectrum analysis.
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Book details

List price: $185.00
Edition: 2nd
Copyright year: 2000
Publisher: John Wiley & Sons, Incorporated
Publication date: 8/12/2013
Binding: Hardcover
Pages: 288
Size: 6.50" wide x 9.75" long x 1.00" tall
Weight: 1.298
Language: English

Introduction
Fourier Analysis
Historical Development of Fourier Methods
Why Use Trigonometric Functions?
Fitting Sinusoids
Curve-Fitting Approach
Least Squares Fitting of Sinusoids
Multiple Periodicities
Orthogonality of Sinusoids
Effect of Discrete Time: Aliasing
Some Statistical Results
Appendix
The Search for Periodicity
Fitting the Frequency
Fitting Multiple Frequencies
Some More Statistical Results
Appendix
Harmonic Analysis
Fourier Frequencies
Discrete Fourier Transform
Decomposing the Sum of Squares
Special Functions
Smooth Functions
The Fast Fourier Transform
Computational Cost of Fourier Transforms
Two-Factor Case
Application to Harmonic Analysis of Data
Examples of Harmonic Analysis
Variable Star Data
Leakage Reduction by Data Windows
Tapering the Variable Star Data
Wolf's Sunspot Numbers
Nonsinusoidal Oscillations
Amplitude and Phase Fluctuations
Transformations
Periodogram of a Noise Series
Fisher's Test for Periodicity
Appendix
Complex Demodulation
Introduction
Smoothing: Linear Filtering
Designing a Filter
Least Squares Filter Design
Demodulating the Sunspot Series
Complex Time Series
Sunspots: The Complex Series
Appendix
The Spectrum
Periodogram Analysis of Wheat Prices
Analysis of Segments of a Series
Smoothing the Periodogram
Autocovariances and Spectrum Estimates
Alternative Representations
Choice of a Spectral Window
Examples of Smoothing the Periodogram
Reroughing the Spectrum
Appendix
Some Stationary Time Series Theory
Stationary Time Series
Continuous Spectra
Time Averaging and Ensemble Averaging
Periodogram and Continuous Spectra
Approximate Mean and Variance
Properties of Spectral Windows
Aliasing and the Spectrum
Analysis of Multiple Series
Cross Periodogram
Estimating the Cross Spectrum
Theoretical Cross Spectrum
Distribution of the Cross Periodogram
Distribution of Estimated Cross Spectra
Alignment
Appendix
Further Topics
Time Domain Analysis
Spatial Series
Multiple Series
Higher Order Spectra
Nonquadratic Spectrum Estimates
Incomplete and Irregular Data
References
Author Index
Subject Index