THE DETERMINATION OF PERIODICITIES IN SHORT-TERM TIME-SERIES DATA IN THE PRESENCE OF HIGH FREQUENCY NOISE AND LONG-TERM TREND

The presence of periodicities in biological data may often be obscured by superposition of a background trend or high frequency oscillations. A method of least squares curve fitting was utilized to remove the trend in signal level. Subsequent removal of higher frequency noise utilizing smoothing convolution functions allows the determination of rhythmic components. A new “noise” convolution function gives a measure of the noise in data containing both signal and noise and allows the estimation of a limit above which an observed oscillation is considered significant. The effects of treating data with these convolution functions are discussed with reference to amplitude-frequency response curves. The results of data analysis utilizing convolution functions are compared with results obtained utilizing a moving interval Fourier technique (Blume, 1965). The convolution analysis have the advantages that they are easily programmed and rapidly calculated by programmable calculators, give results relatively insensitive to the length of convolution interval, and allow estimation of the variation in period and amplitude of the rhythm investigated.