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Coherence Modified for Sensitivity to Relative Phase of Real Band-Limited Time Series

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DOI: 10.4236/am.2014.517261    4,882 Downloads   5,232 Views   Citations
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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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