Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- 1 What Is Fourier Analysis?
- 2 Covariance-Based Approaches
- 3 Fourier Series
- 4 Fourier Transforms
- 5 Using the FFT to Identify Periodic Features in Time-Series
- 6 Constraints on the FFT
- 7 Stationarity and Spectrograms
- 8 Noise in Time-Series
- 9 Periodograms and Significance
- Appendix A DFT Matrices and Symmetries
- Appendix B Simple Spectrogram Code
- Further Reading and Online Resources
- References
- Index
9 - Periodograms and Significance
Published online by Cambridge University Press: 01 February 2019
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- 1 What Is Fourier Analysis?
- 2 Covariance-Based Approaches
- 3 Fourier Series
- 4 Fourier Transforms
- 5 Using the FFT to Identify Periodic Features in Time-Series
- 6 Constraints on the FFT
- 7 Stationarity and Spectrograms
- 8 Noise in Time-Series
- 9 Periodograms and Significance
- Appendix A DFT Matrices and Symmetries
- Appendix B Simple Spectrogram Code
- Further Reading and Online Resources
- References
- Index
Summary
Extends previous chapters with consideration of unequal-interval data and use of periodogram approaches, Schuster and Lomb-Scargle periodograms. Periodograms as examples of least-squares spectral analysis (LSSA) and criteria for statistical significance (p-value). Development of statistical effect-size and significance ideas from periodograms and correlation-regression approaches and application to DFT/FFT power spectra coefficients. Variance spectrum and proportion of variance explained by DFT/FFT frequency components, statistical significance (p-value) of DFT/FFT frequency components.
- Type
- Chapter
- Information
- A Primer on Fourier Analysis for the Geosciences , pp. 137 - 158Publisher: Cambridge University PressPrint publication year: 2019