Analysis of frequency components in time series data

We describe a method for assessing the periodic elements of variations in a time series and illustrate it with examples drawn from infant cardiac beat-to-beat intervals. Compared with averaging techniques, the procedure has the advantage of providing quantification of periodical elements in a non-stationary time series. Moreover, the procedure is robust to artifacts such as those which frequently contaminate beat-to-beat interval data. The method examines successive increments of the time-series plot, and when they become negative or positive, peaks and troughs are noted in the curve. Two successive troughs confine a wave which may be described by its amplitude and period. The set of all waves, terminated by the sequence of troughs, is defined as the "high-frequency component" of the series. Waves of the next low-frequency component are delineated when only the high-frequency peaks (or troughs) are considered. Thus, low-frequency peaks are defined as peaks of the curve formed by the high-frequency peaks, and lower-frequency troughs are the troughs of the curve formed by the high-frequency troughs. The process iterates to assess variations at lower and lower frequencies and any specific frequency component is being characterized by the median and interquartile range of its wave amplitudes and wave periods.