Effects of A/D converter resolution in signal averaging

Abstract

Signal averaging is investigated for the case of a sample-and-sum averager where errors are introduced by the finite amplitude and resolution capabilities of the analog-to-digital (A/D) converter. This is a refinement of a previous treatment [R. R. Ernst, Rev. Sci. Instrum. 36, 1689 (1965)] where the summed signal is an integrated average over the width of each channel. It is shown that when the noise amplitude is much larger than the least significant digit of the A/D converter the original signal is given back after averaging along with two error voltages - one depending on the resolution, and the other on the maximum allowable input to the A/D converter. The expressions given for the magnitudes of the error voltages show that under most laboratory situations the signal can be recovered with high precision - much greater than the resolution of the A/D converter. Also, a general expression for noise in the time averaged output is derived and evaluated for the case of bandwidth-limited white noise. The result shows that the signal averaged noise is small for a low resolution A/D converter and approaches a limiting value for a high resolution converter. Finally, these results are applied to the operation of a high resolution digital voltmeter.