A theory of nonsubtractive dither

A detailed mathematical investigation of multibit quantizing systems using nonsubtractive dither is presented. It is shown that by the use of dither h aving a suitably chosen probability density function, moments of the total error can be made independent of the system input signal but that statistic al independence of the error and the input signals is not achievable. Simil arly, it is demonstrated that values of the total error signal cannot gener ally be rendered statistically independent of one another but that their jo int moments can be controlled and that, in particular, the error sequence c an be rendered spectrally white. The properties of some practical dither si gnals are explored, and recommendations are made for dithering in audio, vi deo, and measurement applications. The paper collects all of the important results on the subject of nonsubtractive dithering and introduces important new ones with the goal of alleviating persistent and widespread misunderst andings regarding the technique.