Fourier analysis of time series : an introduction

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Fourier analysis of time series : an introduction / Peter Bloomfield

資料種別:: 図書
出版情報:: New York : Wiley, c1976
形態:: xiii, 258 p. ; 24 cm
シリーズ名:: Wiley series in probability and mathematical statistics ; . Applied probability and statistics <BA00019013>
著者名:: Bloomfield, Peter, 1946- <DA00979930>
ISBN:: 9780471082569 [0471082562]
書誌ID:: BA00492350

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注記:

Bibliography: p. 247-250
Includes index

主題:

Fourier analysis; Time-series analysis

言語:

英語

目次情報:

Introduction / 1：

Fourier Analysis / 1.1：

Historical Development of Fourier Methods / 1.2：

Why Use Trigonometric Functions? / 1.3：

Fitting Sinusoids / 2：

Curve-Fitting Approach / 2.1：

Least Squares Fitting of Sinusoids / 2.2：

Multiple Periodicities / 2.3：

Orthogonality of Sinusoids / 2.4：

Effect of Discrete Time: Aliasing / 2.5：

Some Statistical Results / 2.6：

Appendix

The Search for Periodicity / 3：

Fitting the Frequency / 3.1：

Fitting Multiple Frequencies / 3.2：

Some More Statistical Results / 3.3：

Harmonic Analysis / 4：

Fourier Frequencies / 4.1：

Discrete Fourier Transform / 4.2：

Decomposing the Sum of Squares / 4.3：

Special Functions / 4.4：

Smooth Functions / 4.5：

The Fast Fourier Transform / 5：

Computational Cost of Fourier Transforms / 5.1：

Two-Factor Case / 5.2：

Application to Harmonic Analysis of Data / 5.3：

Examples of Harmonic Analysis / 6：

Variable Star Data / 6.1：

Leakage Reduction by Data Windows / 6.2：

Tapering the Variable Star Data / 6.3：

Wolf's Sunspot Numbers / 6.4：

Nonsinusoidal Oscillations / 6.5：

Amplitude and Phase Fluctuations / 6.6：

Transformations / 6.7：

Periodogram of a Noise Series / 6.8：

Fisher's Test for Periodicity / 6.9：

Complex Demodulation / 7：

Smoothing: Linear Filtering / 7.1：

Designing a Filter / 7.3：

Least Squares Filter Design / 7.4：

Demodulating the Sunspot Series / 7.5：

Complex Time Series / 7.6：

Sunspots: The Complex Series / 7.7：

The Spectrum / 8：

Periodogram Analysis of Wheat Prices / 8.1：

Analysis of Segments of a Series / 8.2：

Smoothing the Periodogram / 8.3：

Autocovariances and Spectrum Estimates / 8.4：

Alternative Representations / 8.5：

Choice of a Spectral Window / 8.6：

Examples of Smoothing the Periodogram / 8.7：

Reroughing the Spectrum / 8.8：

Some Stationary Time Series Theory / 9：

Stationary Time Series / 9.1：

Continuous Spectra / 9.2：

Time Averaging and Ensemble Averaging / 9.3：

Periodogram and Continuous Spectra / 9.4：

Approximate Mean and Variance / 9.5：

Properties of Spectral Windows / 9.6：

Aliasing and the Spectrum / 9.7：

Analysis of Multiple Series / 10：

Cross Periodogram / 10.1：

Estimating the Cross Spectrum / 10.2：

Theoretical Cross Spectrum / 10.3：

Distribution of the Cross Periodogram / 10.4：

Distribution of Estimated Cross Spectra / 10.5：

Alignment / 10.6：

Further Topics / 11：

Time Domain Analysis / 11.1：

Spatial Series / 11.2：

Multiple Series / 11.3：

Higher Order Spectra / 11.4：

Nonquadratic Spectrum Estimates / 11.5：

Incomplete and Irregular Data / 11.6：

References

Author Index

Subject Index

Introduction / 1：

Fourier Analysis / 1.1：

Historical Development of Fourier Methods / 1.2：

Why Use Trigonometric Functions? / 1.3：

Fitting Sinusoids / 2：

Curve-Fitting Approach / 2.1：

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