The instantaneous frequency of cardiovascular time series: a comparison of methods

The instantaneous frequency (IF) of cardiovascular time series is used to describe the time-varying spectral contents of the characteristic frequency bands that are of interest for psychophysiological and cardiovascular research. Four methods to compute IF of band-limited, monocomponent, and analytical cardiovascular time series were compared by means of simulated time series contaminated with additive noise. These four methods are: the method using the inverse Fourier transform of uncorrelated time-slices of the Wigner-Ville distribution, the discrete time-frequency transform, the circular mean direction of the time-slices of the Wigner-Ville distribution, and the central finite difference of the phase. The time resolution of the estimates is optimal and is inversely related to the bandwidth of the frequency components, as given by the uncertainty principle of Gabor. At periods in time where the signal fulfills the requirements of the model signal, the four estimates of IF are numerically equal; only the circular mean direction showed a slight deviation from the other estimates. Although the estimates of IF differ at sudden phase shifts at low amplitude, i.e. at points where the signal locally does not comply with the requirements of the model signal, overall the four methods produce comparable estimates of IF of a cardiovascular time series at an optimal time resolution.