The tenth short-course in this highly successful sequence of Fourier-focused short-courses will consider two important basic techniques for analysis of geoscience (and other) time-series with regard to periodic features. First, the Fast Fourier Transform (FFT) for equal-interval time-series. Second, the related Lomb-Scargle periodogram for unequal-interval time-series.
The FFT is a key underpinning technique of time-series analysis for the identification of periodic features. The session will overview the key properties of the FFT and the inherent constraints of discrete time-series and sampled data to provide a framework for understanding other, more advanced data-analytical techniques. The Lomb-Scargle periodogram is a least-squares spectral analysis (LSSA) technique and can be considered as a replacement for the FFT for unequal-interval time-series. The session will make the links between the Lomb-Scargle periodogram and the FFT and their common roots in the covariance of a time-series and sinusoids of given frequencies. Both techniques yield estimates of the power spectrum of the data in question and the session will include a consideration of the relationship between the power spectrum and the frequency distribution of the variance as a basis for assessing the statistical effect-size of periodic features in time-series.
This is the tenth in a sequence of short-courses that has resulted in the book "A Primer on Fourier Analysis for the Geosciences", by Robin Crockett, Cambridge University Press. Publication 14 February 2019. https://doi.org/10.1017/9781316543818