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
3 - Fourier 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
Starts with statement of the real Fourier series and orthogonality conditions. Develops the complex Fourier series and introduces the concept of negative frequency, with emphasis as a mathematical convenience, and symmetry of positive-negative frequency coefficients. Concepts of symmetry and linearity. Discrete frequencies and nature of discrete frequency spectrum as comprised of specific fundamental and harmonic frequencies.
- Type
- Chapter
- Information
- A Primer on Fourier Analysis for the Geosciences , pp. 31 - 45Publisher: Cambridge University PressPrint publication year: 2019