Statistical analysis of a linear relation between noisy repetitive signals

This paper deals with the coherence function in order to study relations between channels, in the context of auditory evoked potentials, and more specifically with the statistical analysis of a coherence estimator applied to signals having periodicity. In practice, a stimulus is periodically sent and a sufficient number of individual responses are recorded to increase the signal-to-noise ratio. In this way, a coherence estimator can be defined. Under some hypotheses, we get a simplified version of this quantity and we study its distribution and its mean. Simulations illustrate theoretical results. Then, we estimate the mean value of the coherence computed on a given number of responses. We derive the bias versus the theoretical coherence and the number of individual responses.