njit-etd2003-081 - New Jersey Institute of Technology

91
standard error for the estimated delay. In this dissertation, phase spectra are not being
considered. However, these studies of the phase curves and their slopes obtained from
correlation between two physiological signals such as HR and Respiration, BP and
Respiration or HR and BP can be performed in the future. This will help in
understanding the time delay, phase lead or phase lag between the regulatory systems
that cause the changes in HR, BP and respiration.
3.11 Weighted Coherence
Weighted coherence is defined by Porges et al. (1980) as the proportion of the total
variance of one signal that is shared with the other signal within a certain frequency
band [51]. It can be computed easily from the values of the coherence function and the
spectral density values of one of the signals in that frequency region. It has the
advantage that one measure can be derived for a whole frequency band of interest, for
example the low or high frequency band of the heart rate variability spectrum. The
weighted coherence function can be computed by the following formula:
In which:
CWxy (f 1, f 2) = Weighted coherence in the frequency band between fl and f2
CohXY (f) = Coherence between the signals x and y for frequency f
Pyy (f) = Power spectral density of the signal y for frequency f.