Coherence and transfer function estimation in cardiovascular variability analysis: a comparison between the classical and autoregressive approach

The authors compared by a computer simulation the accuracy of the magnitude squared coherence (MSC) function and of the gain and phase spectrum estimated by the Blackman-Tukey (BT) and autoregressive (AR) methods. Two stochastic processes were generated by AR fitting a real systolic pressure signal and a synthetic signal both containing a very low frequency (0.01-0.04 Hz), a low frequency (0.04-0.15 Hz) and a high frequency (0.15-0.45 Hz) component, passed through a linear block with known transfer function and added to a white noise source. The synthetic signal was characterized by narrower spectral peaks in order to stress the resolving power of the estimated functions. For each process 300 realizations at a record length of 3 and 5 min were generated, the corresponding system output computed and the MSC, gain and phase at the 3 spectral components estimated. The error in the estimation of the gain and phase shift was negligible at all frequencies for both AR and BT. In the estimation of the MSC, AR performed better than BT, which showed a systematic negative bias and a lower spectral resolution.