The SNR of ABR Signals

Authors: Malcolm Slaney1, Emily Kuo1, Gavin Bidelman2, Dáibhid Maoiléidigh1

1Stanford University
2Indiana University

Background: We are interested in the statistical properties of auditory brainstem responses (ABR). ABR analysis often looks for features of the averaged waveform (Bidelman, 2018), or is trying to decide whether an ABR is present in a recording (Elberling, 1987). In this work we summarize results of a statistical analysis of ABR recordings, over and above that of Elberling’s work, in order to estimate the underlying signal and noise levels. From these estimates we can derive an estimate of the accuracy of the signal estimate.

Methods: We express the measured ABR voltage as a sum of a deterministic signal s(t) and a Gaussian noise, with constant variance n^2. There are two parts of our derivation: estimating the latent signal and noise using a regression approach, and deriving an estimate of the accuracy of the signal average.

Results: Averaging the ABR responses to estimate the underlying signal reduces the noise power, but doesn’t eliminate it. The average signal power at each point in time is s^2 + n^2/N, where N is the number of trials. This is summarized in Figure 1, which shows that the average power is a blend of the noise and the signal levels. This blend limits the accuracy of the signal estimate, which is shown as a potential relative error (+/-1 standard deviation) in Figure 2. For one subject from the Bidelman data, we estimate that the maximum SNR is -14dB, and with 6000 trials the potential error is 5%. When we don’t have infinite data, we still want to estimate the signal and noise levels. We derive a regression approach based on a subset of the number of trials. Figure 3 shows that when we have fewer than 200 trials the regression approach is more accurate than the conventional asymptotic approach.

Conclusions: We have the start of a more robust statistical analysis of ABR signals, from which we hope to put ABR analysis on a firmer footing.