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
- References
Further Reading and Online Resources
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
- References
Summary
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- A Primer on Fourier Analysis for the Geosciences , pp. 170 - 171Publisher: Cambridge University PressPrint publication year: 2019
References
Further Reading and Online Resources
There are many books on Fourier theory and I cannot hope to list even all the introductory ones. This is a list of books that I have used over the years and have found useful – no more or less than that. My advice is to look around and find books that deal with aspects of the subject relevant to you in a manner that is accessible to you – and I hope that this book gives you a starting-point for accessing more advanced texts with confidence.
Dyke, P. (2014) An Introduction to Laplace Transforms and Fourier Series (2nd ed.), Springer Undergraduate Mathematics Series, Springer-Verlag London, ISBN:978–1–4471–6394–7.Google Scholar
Gabel, R. A. and Roberts, R. A. (1986) Signal and Linear Systems (3rd ed.), Wiley, ISBN:978–9–9715–1167–8.Google Scholar
James, J. F. (2011) A Student’s Guide to Fourier Transforms: With Applications in Physics and Engineering (3rd ed.), Cambridge University Press, ISBN:978–0–5211–7683–5.Google Scholar
Kuo, F. (1966) Network Analysis and Synthesis (2nd ed.), Wiley, republished Wiley India Pvt. Limited, 2006, ISBN:978–8–1265–1001–6.Google Scholar
McQuarrie, D. A. (2003) Mathematical Methods for Scientists and Engineers, University Science Books, ISBN:978–1–8913–8929–7.Google Scholar
Newland, D. E. (1993) An Introduction to Random Vibrations, Spectral & Wavelet Analysis (3rd ed.), Longman, London, republished 2005 Dover, ISBN:978–0–4864–4274–7.Google Scholar
Proakis, J. G. and Manolakis, D. K. (2009) Digital Signal Processing (4th ed.), Pearson, ISBN:978–0–1322–8731–9.Google Scholar
Riley, K. F. (1974) Mathematical Methods for the Physical Sciences: An Informal Treatment for Students of Physics and Engineering, Cambridge University Press, ISBN:978–1–1391–6755–0.Google Scholar
Wirsching, P. H., Paez, T. L and Ortiz, K. (1995) Random Vibrations: Theory and Practice, John Wiley & Sons, New York, republished 2006 Dover, ISBN:978–0–4864–5015–5.Google Scholar
Online Resources
URL for the R software, documentation and manuals.
The R Project for Statistical Computing, www.r-project.org.
URLs for two comprehensive and accessible online resources I recommend to research students. There are many others to choose from.
Bourke, P. (1993). DFT (Discrete Fourier Transform) FFT (Fast Fourier Transform), http://paulbourke.net/miscellaneous/dft.Google Scholar
Shatkay, H. (1995). The Fourier Transform – A Primer. Technical Report. Brown University, USA, ftp://ftp.cs.brown.edu/pub/techreports/95/cs95–37.pdf. (Postscript versions also available.)Google Scholar
URLs for sources of data. These URLs were all live at the time of writing but it is likely that some will change with the passage of time.Google Scholar
Tidal data are available from the Australian Baseline Sea-Level Monitoring Project (ABSLMP), www.bom.gov.au/oceanography/projects/abslmp/data/index.shtml.Google Scholar
Regularly updated sunspots data are available from WDC-SILSO, Royal Observatory of Belgium, www.sidc.be/silso/datafiles.Google Scholar
Global mean land-ocean temperature data are available from the NASA Goddard Institute for Space Studies, http://data.giss.nasa.gov/gistemp/graphs.Google Scholar
Beryllium-10 solar-irradiance proxy data are available from the World Data Center for Paleoclimatology, Boulder, and NOAA Paleoclimatology Program, ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/greenland/summit/ngrip.Google Scholar
Climate data, e.g. Dubuque temperature data, are available from the Iowa State University Mesonet, http://mesonet.agron.iastate.edu/climodat/index.phtml?station=ia2364&report=16.Google Scholar
Mauna Loa atmospheric CO2 data are available from the Carbon Dioxide Information Analysis Center, http://cdiac.ess-dive.lbl.gov/ftp/maunaloa-co2.Google Scholar
Canadian atmospheric CO2 data for Alert, Northwest Territories, are available from the Carbon Dioxide Information Analysis Center, http://cdiac.ess-dive.lbl.gov/ftp/trends/co2/altsio.co2.Google Scholar
The star data, and other datasets, are available from The University of Minnesota, Duluth, www.d.umn.edu/~skatsev/Phys5053/Datasets.html.Google Scholar
USGS water resource data, including the Iowa river flow data, are available from the National Water Information System, http://waterdata.usgs.gov/ia/nwis/sw.Google Scholar
Monthly Atmospheric and SST Index Values are available from the NOAA Climate Prediction Center, www.cpc.ncep.noaa.gov/data/indices.Google Scholar
Various tree-rings and other datasets are available from the Time Series Data Library, https://datamarket.com/data/list/?q=provider:tsdl.Google Scholar
Delta-18O data are available from the NOAA National Centers for Environmental Information, ftp://ftp.ncdc.noaa.gov/pub/data/paleo/contributions_by_author/shackleton1990.Google Scholar
The exoplanet data are available from the Penn State University Center for Astrostatistics, http://astrostatistics.psu.edu/datasets/exoplanet_Doppler.html.Google Scholar