AM  Vol.5 No.17 , October 2014
Coherence Modified for Sensitivity to Relative Phase of Real Band-Limited Time Series
Author(s) William Menke
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.

Cite this paper
Menke, W. (2014) Coherence Modified for Sensitivity to Relative Phase of Real Band-Limited Time Series. Applied Mathematics, 5, 2739-2745. doi: 10.4236/am.2014.517261.
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