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

• 作者: William Menke
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Time Series COHERENCE CROSS CORRELATION Band-Limited MONOCHROMATIC FILTER
• 年，卷（期）: 2014,（17）
• 页码范围: 2739-2745
• 页数: 7页
• 分类号: O1

摘要

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.