The trigonometric regressive spectral analysis : A method for mapping of beat-to-beat recorded cardiovascular parameters on to frequency domain in comparison with Fourier transformation

Heart rate and peripheral blood pressure as physiological recorded vegetative parameters are very often rhythmically investigated with the Fourier Transformation (FT). In contrast to the original use of FT these parameters are still stochastic with overlaying rhythmical structures. The R-R intervals as independent variables of time are not equidistant. The mathematical structure for the spectral decomposition is critically analysed. The purpose of this article is the presentation of a mathematical method, considering both the statistical and rhythmical features of such time series. On the basis of trigonometric regressions, this method is presented to eliminate the equidistance problems, arising with the usage of FT, by a new mathematical approach. This method computes more precisely the spectral power especially in the VLF range (0.003-0.04 Hz) than FT, because this method of trigonometric regression does not perform a frequency quantization. This method has been used and successfully tested for the analysis of peripheral blood pressure and R-R intervals including an effective reduction of input data.