Equivalence of Widrow's and Gray's approaches to uniform quantizers

Abstract

In the paper we demonstrate the equivalence between Widrow's and Gray's approaches to the quantization error created in a uniform quantizer by the pure sine wave with a random initial phase and a deterministic bias. The exact finite-sum formulas are directly derived from the infinite-sum series resulting from the classical Quantization Theory. The analytical results lead to the simplification of data processing recommended by the IEEE Standards.