Interpretation and use of coherence in multi-channel measurements

The coherence function can be a powerful tool when analyzing data from multi-channel measurements. Often, coherence is used to describe the amount of incoherent noise in an output signal, though more generally the coherence between two signals is a representation of the linearity of the relationship between the signals as a function of frequency. Such degradation in the coherence then can be understood to not only be caused by potential incoherent noise, but also by moving sensors or a changing acoustic environment. Aside from its use as a diagnostic tool, coherence can also be used to condition measured data. For example, a sensor can be placed on a source of unwanted sound, and the portion of the desired signal coherent with the sensor's output (the "coherent output power") can be removed. In this paper, methods for coherent noise removal and signal enhancement are presented in both the frequency and time domains. Example measurements are used to demonstrate the effectiveness of the techniques for situations where separating noise sources is otherwise difficult.