A framework for assessing the relative efficiency of stimulus sequences in evoked response measurements

A general matrix-based framework for characterizing the performance of cross-correlation techniques for recovering the response to an arbitrary stimulus sequence is presented. In general an infinite number of recovery sequences can be identified for any given stimulus sequence. The recovery sequence that minimizes the noise in the recovered response is derived and the effect of the recovery operation on the noise is analyzed. This general framework is employed to develop analytic expressions for the relative efficiencies of conventional signal averaging and binary MLS based methods for the most commonly used recovery operation and the one that optimizes SNR assuming the background noise is uncorrelated. The results depend on the ratio of response length to MLS minimum pulse interval and the amplitude loss as a function of stimulus rate. Examples based on measured amplitude loss functions for ABR recordings are employed to evaluate the relative efficiencies of MLS techniques. When the noise is uncorrelated conventional signal averaging is from two to five times as efficient as MLS techniques. The relative advantage of averaging is shown to decrease when the noise is dominated by low-frequency components.