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