Roundoff Errors in Signal Averaging Systems

In biomedical signal averaging applications where a small repetitive signal is to be extracted form a very noisy waveform (noise variance σ
²
_n
), the A/D converter range is set at ±Aσ
_n
where A typically has a value of 3 or 4. In this case, A/D roundoff noise using a (b + 1)-bit A/D converter degrades the SNR of the resulting signal estimate by an amount slightly greater than 10 log (1 + A
²
2
^-2b
/12). Application of this result to the design of a system for digital acquisition and averaging of the acoustic brainstem response indicates that an increase of A/D resolution beyond the first few bits yields little improvement in the SNR of the measurement.