The Discrete Fourier Transform (DFT) in Behavioural Analysis

Spectral analysis is an important tool for examining time-series data and can be particularly powerful in detecting periodicity in animal behaviour patterns. Because of its simplicity and the speed of current computing algorithms, the discrete Fourier transform is most often used in spectral analysis. An understanding of several important aspects of discrete Fourier transform analysis (its application to degenerate or transformed data, aliasing, truncation, and statistical inference) is central to the appropriate use of this form of spectral analysis. These aspects are discussed and evaluated in the context of the analysis of temporal behaviour patterns of animals. The variety of published techniques for the statistical analysis of discrete Fourier transform spectra is particularly vexing for behavioural scientists interested in the possible significance of individual components (peaks): a conservative and simple χ2 test is proposed as a solution.