Coherence Function

The coherence function provides an indication of the quality of the frequency response function measurement and of how much of the response energy is correlated to the stimulus energy. If there is another signal present in the response, either from excessive noise or from another signal, the quality of the network response measurement is poor. You can use the coherence function to identify both excessive noise and which of the multiple signal sources are contributing to the response signal. Use the following equation to compute the coherence function.

where S_AB is the cross power spectrum, S_AA is the power spectrum of A, and S_BB is the power spectrum of B.

The previous equation yields a coherence factor with a value between zero and one versus frequency. A value of zero for a given frequency line indicates no correlation between the response and the stimulus signal. A value of one for a given frequency line indicates that 100% of the response energy is due to the stimulus signal and that no interference is occurring at that frequency.

For a valid result, the coherence function requires an average of two or more readings of the stimulus and response signals. For only one reading, the coherence function registers unity at all frequencies.