Coherence Weighted Decibel Averaging (Transfer Function)

Coherence weighted dB magnitude response averaging is the default selection for transfer function spatial averages and works well for most applications. In a coherence weighted dB average, each data point in every measurement being averaged is weighted according to its coherence value. Coherence is technically an estimation of linearity in transfer function measurements. In practical terms, it tends to be an indicator of a signal-to-noise ratio and so higher coherence suggests that the data is more trustworthy.

When averaging data from multiple microphone positions, if one measurement has poor coherence at some frequencies due to nulls in a comb filter, localized reverberant buildup, or perhaps it was taken near the edge of the coverage pattern of a loudspeaker where the HF response was rolling off, coherence weighting should result in the most trustworthy frequencies contributing more to the average than more problematic frequencies. 

In otherwise well-behaved measurement environments, when comb filtering at individual measurement positions is a significant issue – e.g., due to a floor or ceiling bounce – coherence weighted dB averaging and normalized power averaging will tend to produce similar results because the signal-to noise ratio of the measurements will tend to be higher in the lobes and poorer in the nulls. Power averaging, however, is unable distinguish uncorrelated energy from the system response and coherence weighted averaging requires no assumptions regarding the frequency range of the device or system under test.

See also: What is Coherence?

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