Teaching time-series analysis. I. Finite Fourier analysis of ocean waves

Abstract

The introduction of students to methods of time-series analysis is a pedagogical challenge, since the availability of easily manipulated computer software presents an attractive alternative to an understanding of the computations, as well as their assumptions and limitations. A two-part pedagogical tutorial exercise is offered as a hands-on laboratory to complement classroom discussions or as a reference for students involved in independent research projects. The exercises are focused on the analysis of ocean waves, specifically wind-generated surface gravity waves. The exercises are cross-disciplinary in nature and can be extended to any other field dealing with random signal analysis. The first exercise introduces the manual arithmetic steps of a finite Fourier analysis of a wave record, develops a spectrum, and compares these results to the results obtained using a fast Fourier transform (FFT). The second part of the exercise, described in the subsequent article, takes a longer wave record and addresses the theoretical and observed wave probability distributions of wave heights and sea surface elevations. These results are then compared to a FFT, thus linking the two pedagogical laboratory exercise parts for a more complete understanding of both exercises.