Author(s)

William Menke

Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY, USA.

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.

Time Series, Coherence, Cross Correlation, Band-Limited, Monochromatic, Filter

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.