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
2 - Covariance-Based Approaches
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
Review of correlation and simple linear regression. Introduction to lagged (cross-) correlation for identifying recurrent and periodic features in common between pairs of time-series, statistical evidence of possible causal relationships. Introduction to (lagged) autocorrelation for identifying recurrent and periodic features in time-series. Use of correlation and simple linear regression for statistical comparison of time-series to reference datasets, with focus on periodic (sinusoidal) reference datasets. Interpretation of statistical effect-size and significance (p-value).
Keywords
- Type
- Chapter
- Information
- A Primer on Fourier Analysis for the Geosciences , pp. 9 - 30Publisher: Cambridge University PressPrint publication year: 2019