Crockett, R. G. M. (2011) Time-series analysis: how to apply and interpret the fast Fourier transform. Lecture presented to: European Geosciences Union (EGU) General Assembly, Vienna, Austria, 03-08 April 2011. (Unpublished)
United Nations Educational, Scientific and Cultural Organization (UNESCO) / International Union of Geological Sciences (IUGS)
Many natural hazards have cyclic/periodic behaviour, e.g. radon, earthquakes (under some circumstances), annual/seasonal droughts and floods, whereas others are anomalous, apparently random with regard to time, e.g. earthquakes and volcanic eruptions(under most circumstances). For the cyclic cases, an analysis of past time-series can yield an expectation and perhaps some degree of forecasting, even if only at the level of 'more probable' and 'less probable' times of occurrence. This is the background for this short-course: we need to be able to analyse a sequential record of events, i.e. a time-series, for cyclic/periodic features. More specifically, the aim of this short-course is to provide an introduction to and overview of what is arguably the key technique of time-series analysis in this context: the Fast (Discrete) Fourier Transform. The focus will be on application of the Fast Fourier Transform, as implemented in many software packages, and interpretation of the output. Anticipating that most of those who attend will be 'technique users' rather than 'technique developers', coverage of the underlying mathematics will be kept to a necessary minimum to facilitate informed interpretation of the Fast (Discrete) Fourier Transform.