Convenient formulas for quantization efficiency

Abstract

Digital quantization of signals prior to processing results in the insertion of a component of noise resulting from the finite number of quantization levels. In radio astronomy, for example, this is important because the number of levels tends to be limited by increasing sample rates, required by the use of increasingly wide bandwidths. We are here concerned with signals with Gaussian amplitude distribution that are processed by cross correlation. Quantization efficiency is the relative loss in signal‐to‐noise ratio resulting from the quantization process. We provide a method of calculating the quantization efficiency for any number of uniformly spaced levels, as a function of the level spacing, using formulas that are easily evaluated with commonly used mathematical programs. This enables a choice of level spacing to maximize sensitivity or to provide a compromise between the sensitivity and the voltage range of the input waveform.