  A number of popular measures of dependence between pairs of band-limited
signals rely on analytic phase. A common misconception is that the dependence
revealed by these measures must be specific to the spectral range of the
filtered input signals. Implicitly or explicitly, obtaining analytic phase
involves normalizing the signal by its own envelope, which is a nonlinear
operation that introduces broad spectral leakage. We review how this generates
bias and complicates the interpretation of commonly used measures of phase
locking. A specific example of this effect may create spurious phase locking as
a consequence of nonzero circular mean in the phase of input signals, which can
be viewed as spectral leakage to 0 Hz. Corrections for this problem which
recenter or uniformize the distribution of phase may fail when the amplitudes
of the compared signals are correlated. To address the more general problem of
spectral bias, a novel measure of phase locking is proposed, the
amplitude-weighted phase locking value (awPLV). This measure is closely related
to coherence, but it removes ambiguities of interpretation that detract from
the latter.
