A Robust Symmetrical Number System with Gray code properties for applications in signal processing

Abstract

A new symmetrical number system with applications in parallel signal processing is investigated. The Robust Symmetrical Number System (RSNS) is a modular system in which the integer values within each modulus, when considered together, change one at a time at the next position (Gray code properties). Although the observed dynamic range of the RSNS is somewhat less than the optimum symmetrical number system, the Gray code properties make it particularly attractive for folding analog-to-digital converters. With the RSNS, the encoding errors (due to comparator thresholds not being crossed simultaneously) are eliminated, as is the need for the corresponding interpolation signal processing (reduced complexity). Computer generated data is used to help determine the properties of the RSNS. These properties include the largest dynamic range (number of distinct consecutive vectors), and the position of the largest dynamic range within the system. The position of the maximum unambiguous dynamic range is also quantified. Least squares analysis of 2 and 3 moduli systems are used to formulate closed-form expressions for the dynamic range. To compare the advantages of the RSNS with previously published results, the transfer function of a 3 channel RSNS folding analog-to-digital converter architecture (m1 =3, m2 = 4, and m3 = 5) is numerically evaluated using SPICE.