Valid Method to Evaluate the Slope of Fourier Transformed Spectrum for the Analysis of Biological Rhythm Fluctuation

Abstract

Influences of lower frequency components of power spectrum calculated from biological rhythm data on the spectral slope were examined and the validity of conventional method to calculate the spectral slope was tested. Heart-beat-period data obtained from the electrocardiogram of rats were cut into two successive data sets, each of them was converted into power spectrum density by the fast Fourier transform, and the power spectra were compared with each other. The results showed that two spectra were overlapped only in the frequency range higher than a frequency about 15 times that of the dominant one, which means that the lower frequency components are not always the same and thus, the regression line by which the spectral slope is determined is considerably affected by the components. To evaluate the spectral slope, regression lines of spectra were obtained in three methods and their slopes were compared with each other. The methods were: “conventional” method, in which the weight of a frequency component was independent of the frequency (i.e., equal-weight = 1); “weight” method, in which the weight was the wave number included in the rhythm data; and “limited-data” method, where the weight was 1 and lower-frequency components were excluded, The results showed that there was not a large difference between the slopes in cases where the spectrum looked rather linear. However, in cases of considerably curved spectra the difference was large and the “weight” method may be the most reasonable to use, and in cases of short data length the “limited-data” method should be avoided.