# Coherence

- This gives a measure of the linear dependence between signal A and B.
- where
*G*_{AB}= cross-spectrum between signal A and B obtained by averaging*(f)**G*_{AA}and*(f)**G*_{BB}= power spectra of signal A and B obtained by averaging*(f)*

A two channel function which is used when an output (e.g. displacement) is caused by more than one input (e.g. two unrelated forces at different positions). The coherence function shows how much of the output is caused by each of the inputs, as a function of frequency. The value of coherence at any given frequency must lie between 0 and 1. A coherence of 0 between an input and output implies that the output results entirely from other inputs, whereas a coherence of 1 implies that the output results entirely from that input.

For a mechanical measurement between two points, if the structure is linear, the coherence will be one, but if there is some nonlinearity in the structure or if there is noise in a measurement channel, the coherence will be less than one.

This simple relationship does not apply if the inputs themselves are related in some way. In situations where the inputs are not independent, it is necessary to use more complex functions known as partial and multiple coherences. Coherences between two outputs (e.g. displacements at 2 points on a structure) can also be used to check that they result from a common source.

**Reasons for a coherence value < 1:**

- nonlinearities in the system or delays not compensated for
- noise or leakage in the measurement

In the case of cross-correlation and transfer function calculations it is wise to check the coherence which gives a measure of the validity of the assumption that the output signal is related to the input signal.

**Note:** For an averaging number of 1, the coherence is always 1 and gives no valuable information.

A laser is a good example of coherent light. An ordinary light bulb produces incoherent light much like the random waves produced when many raindrops hit a puddle. Electromagnetic radiation is coherent when the photons are produced in such a way that they are in phase with one another and incoherent when the phases of the photons are random. Partial coherence is an intermediate situation where there a significant fraction of the photons have related phase, but not all of them.

**Subjects: ** Noise & Vibration Signal Processing