Spectral analysis of cardiovascular time series by the S-transform

This paper proposes the S transform as a method for spectral analysis of cardiovascular time series. The S transform (ST) is an extension of the Wavelets, it uses an analysis window whose width is decreasing with frequency then providing a frequency dependent resolution (constant Q). This allows to overcome the drawbacks of the Short Time Fourier Transform (STFT) in analyzing non stationary time series like the cardiovascular series as obtained during diagnostic manoeuvres able to 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 to 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 to discriminate specific components related to low rate respiratory activity from other low frequency oscillations.