Biological time-series data pertaining to human circadian and ultradian hormonal rhythms are often short, sparse, irregularly spaced, and noisy. In addition, they often have missing data points and have variable experimental uncertainties. The objective of collecting and analyzing such data is to find the amplitude, phase, and period of the primary rhythmic component contained within the data. Often the question is simply: Does a rhythm exist. The theoretical aspects of some Fourier techniques are discussed, including methods for detrending non-stationary time-series and the evaluation of confidence intervals. Analysis of typical biological data are also presented.
Michael L. Johnson,
"Fourier analysis of real-world data", Proc. SPIE 2985, Ultrasensitive Biochemical Diagnostics II, (22 May 1997); doi: 10.1117/12.274356; https://doi.org/10.1117/12.274356