# Coherence¶

Coherence measures the relationship between signals. For a linear system, it can be used to estimate the power transfer between the inputs and outputs. The coherence of two signals is a value between 0 and 1, where 0 suggests no power transfer and 1 represents full power transfer.

For more detailed information about coherence, see: Wikipedia.

Important

The resistics name for the coherence statistic is: **coherence**.

The following components are calculated out:

coh E

_{x}H_{x}coh E

_{x}H_{y}coh E

_{y}H_{x}coh E

_{y}H_{y}

In most cases, the off-diagonals are expected to be small as E_{x} is not expected to significantly impact H_{x} and similarly with E_{y} and H_{y}. Generally, the coherences of interest are between E_{y}-H_{x} and E_{x}-H_{y}. High values of coherence between E_{x}-H_{y} and/or E_{y}-H_{x} often represent good data and time windows with such high values are normally kept for transfer function estimation. However, high coherence values can also be caused by a nearby coherent source of electromagnetic energy.

An example of window-by-window coherence values is shown below.

The above coherence shows a couple of trends:

Generally, E

_{y}-H_{x}is more coherent than E_{x}-H_{y}Near the end of the recording something caused the coherence to fall primarily in E

_{x}coherences. Studying the E_{x}timeseries might provide more clues to the cause of this.

Another way to look at the same data is in the form of a histogram. Ideally, there should be more higher coherent values than lower ones.

Below are two additional plots from a different day long recording at 128 Hz. In this case, the coherence plots show a significant improvement after 16:00. Before this time, there are significant numbers of noisy windows. The noise is probably cultural and due to daily human activity.