Spectral analysis of cardiovascular time series by the S-transform

This paper proposes the S transform (ST) as a method for spectral analysis of cardiovascular time series. The ST is an extension of wavelets: it uses an analysis window whose width decreases with frequency thus providing a frequency dependent resolution (constant Q). This allows one to overcome the drawbacks of the short time Fourier transform (STFT) in analyzing nonstationary time series like the cardiovascular series as obtained during diagnostic manoeuvres which change the status of the autonomic nervous system (ANS). The ST maintains a link with the Fourier analysis since its average over time provides the Fourier spectrum. Moreover, it is a linear transform and it provides frequency representation without cross-terms. An evaluation of the ST characteristics was performed by comparison with STFT, evolutionary periodogram and Wigner Ville transform in analyzing specific non-stationary synthetic signals. The method was applied to real cardiovascular time series, like heart rate and systolic pressure, as obtained by patients submitted for autonomic tests; the results showed high time resolution at respiratory frequency allowing the detection of short high frequency components; moreover, the good frequency resolution at low frequency allows one to discriminate specific components related to low rate respiratory activity from other low frequency oscillations