Lipshitz, S.P., R.A. Wannamaker, J. Vanderkooy and J.N. Wright, "Non-Subtractive
Dither," Proc. of the 1991 IEEE Workshop on Applications of Signal Processing
to Audio and Acoustics, New Paltz, NY, 1991 Oct.
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unpublished.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 Brinton, Lipshitz and
Vanderkooy, and Gray. In view of many widespread misunderstandings
regarding non-subtractive dither, it seems that formal presentation
of these results is long overdue.