Delay estimation for cortico-peripheral relations

In neurophysiology, time delays between concurrently measured time series a re usually estimated from the slope of a straight line fitted to the phase spectrum. We point out that this estimate is valid only in the case in whic h, one signal is a mere time-delayed copy of the other one. We present a pr ocedure for delay estimation that applies to a much wider class of systems with nontrivial phase spectrum like for example lowpass filters. The proced ure is based on the Hilbert transform relation between the phase of a linea r system and its log gain. The Hilbert transform relation is nonlocal in fr equency space, a fact that limits its applicability to experimental data. W e explore these limits, and demonstrate that the method is applicable to ne urophysiological time series. We present the successful application of the Hilbert transform behavior method to concurrently recorded epicortical brai n activity and peripheral tremor. We point out and explain physiologically unreasonable delay estimates given by the traditional method. Finally, we d iscuss the assumptions underlying the applicability of the Hilbert transfor m method in tile neuroscience context. (C) 2001 Elsevier Science B.V. All r ights reserved.