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
5 - Using the FFT to Identify Periodic Features in Time-Series
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
Standard form of forward and inverse Fast Fourier Transform (FFT). Sets up a systematic approach for generating frequency indices and calibrated frequencies for FFT spectra. Develops systematic approach for generating and interpreting amplitude and power spectra as vectors in a complete FFT output data-table with frequency indices. Worked examples using real time-series as typify ‘clean’ and ‘noisy’ data, data with single and multiple frequencies, data with trends.
- Type
- Chapter
- Information
- A Primer on Fourier Analysis for the Geosciences , pp. 69 - 91Publisher: Cambridge University PressPrint publication year: 2019