We assume that both of the nonreferential signals b1(t) and b2(t) are not correlated with the reference signal R(t). In this case, based on (5), we can write the MSC of referential signals x1 and x2 as (11)MSCx1x2=(Sb1b2(w)+SRR(w))2(Sb1b1(w)+SRR(w))(Sb2b2(w)+SRR(w)) (see [34] and [36] for details). From (11), an upper bound can be derived as follows: (12)MSCx1x2≤(∣Sb1b2(w)∣+SRR(w))2(Sb1b1(w)+SRR(w))(Sb2b2(w)+SRR(w)) which has been previously reported [36]. The authors [36] employed this bound to examine the effect of the reference signal R(t) on the MSC of nonreferential signals b1(t) and b2(t) and argue that, under the assumption that the scalp reference signal is not correlated with the iEEGs being studied, the reference signal will have a limited impact upon coherence measurements when the power of the reference signal is smaller than the power of the intracranial signals at every frequency. However, in the following, we show that the conclusion is true only for positive cross correlations in (11). The reason is that the cross-power Sb1b2(w) may be negative, and in (12), only the absolute value of the cross-power Sb1b2(w) is used. In (11), if we further
