TITLE:
Coherence Modified for Sensitivity to Relative Phase of Real Band-Limited Time Series
AUTHORS:
William Menke
KEYWORDS:
Time Series, Coherence, Cross Correlation, Band-Limited, Monochromatic, Filter
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.17,
October
23,
2014
ABSTRACT: As is well known, coherence does not distinguish the relative phase of a pair of real, sinusoidal time series; the coherence between them is always unity. This behavior can limit the applicability of coherence analysis in the special case where the time series are band-limited (nearly-monoch- romatic) and where sensitivity to phase differences is advantageous. We propose a simple mod-ification to the usual formula for coherence in which the cross-spectrum is replaced by its real part. The resulting quantity behaves similarly to coherence, except that it is sensitive to relative phase when the signals being compared are strongly band-limited. Furthermore, it has a useful interpretation in terms of the zero-lag cross-correlation of real band-passed versions of the time series.