Hybrid-Computer Techniques for Measuring Statistics from Quantized Data

Abstract

Digital data processing necessarily involves quantization (roundoff) of input data. The statistical theory of amplitude quantization indicates that the effects of quantization on statistics are often negligible or can be approximately predicted and corrected, even with surprisingly coarse quantization. This tutorial paper reviews contributions to the theory made in England, the Netherlands, and Russia, as well as B. Widrow's original work in this country. Applications to remarkably inexpensive hybrid analog-digital averaging computers and correlators are also discussed. The theory can pay very handsome practical dividends: in many applications, 2- to 4-bit analog-to-digital converters and data-transmission channels can yield averages, mean squares, and correlation functions with 10- to 20-bit accuracy, and one-bit (polarity-coincidence) correlators are often practical.