A Primer on Fourier Analysis for the Geosciences

An intuitive introduction to basic Fourier theory, with numerous practical applications from the geosciences and worked examples in R.

Robin Crockett (Author)

9781316600245, Cambridge University Press

Paperback / softback, published 14 February 2019

188 pages, 72 b/w illus.
22.8 x 15.1 x 1 cm, 0.31 kg

'This is a perfect book for researchers wanting to know how to perform time series analysis using the Fast Fourier Transform. The examples from Earth sciences and the R codes are especially useful for young scientists and newcomers in the field of time series analysis.' François G. Schmitt, Centre National de la Recherche Scientifique (CNRS), Paris

Time-series analysis is used to identify and quantify periodic features in datasets and has many applications across the geosciences, from analysing weather data, to solid-Earth geophysical modelling. This intuitive introduction provides a practical 'how-to' guide to basic Fourier theory, with a particular focus on Earth system applications. The book starts with a discussion of statistical correlation, before introducing Fourier series and building to the fast Fourier transform (FFT) and related periodogram techniques. The theory is illustrated with numerous worked examples using R datasets, from Milankovitch orbital-forcing cycles to tidal harmonics and exoplanet orbital periods. These examples highlight the key concepts and encourage readers to investigate more advanced time-series techniques. The book concludes with a consideration of statistical effect size and significance. This useful book is ideal for graduate students and researchers in the Earth system sciences who are looking for an accessible introduction to time-series analysis.

Preface
Acknowledgments
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.

Subject Areas: Environmental monitoring [TQD], Oceanography [seas RBKC], Earth sciences, geography, environment, planning [R], Atmospheric physics [PHVJ], Geophysics [PHVG], Mathematical modelling [PBWH]