Non-Subtractive Dither

Abstract

A mathematical investigation of quantizing systems using non-subtractive dither is presented. It is shown that with a suitably-chosen dither probability density function (pdf), certain moments of the total error can be made signal-independent and the error signal rendered white, but that statistical independence of the error and the input signal is not achievable. Some of these results are known but appear to be unpublished. The earliest references to many of these results are contained in manuscripts by one of the authors [JNW'] but they were later discovered independently by Stockham and Brinton2i3, Lipshitz and Vanderkooy4, and Gray5. In view of many widespread misunderstandings regarding non-subtractive dither, it seems that formal presentation of these results is long overdue.