Coherence can be defined as follows:
where is the cross power spectral density of the two signals, x and y, while and are the power spectral densities of x and y, respectively.
Coherence is a function of frequency that measures the degree of linear dependency of two signals by testing whether they contain similar frequency components. The magnitude of coherence ranges from zero to one. At a given frequency, if the coherence is equal to 1 the two signals are considered to correspond to each other perfectly at that frequency. Conversely, a coherence which is equal to 0 suggests that the signals are totally unrelated at that frequency.
For computation, the signal is broken down into several sections for frequency component analysis using FFT. Adjacent sections can overlap, which helps to detect shared frequencies across sections. The size of FFT sections, window type and size, and the number of overlapping data points can affect the result. These choices should be made according to the nature of the input signals.
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