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 having a suitably chosen probability density function, moments of the total error can be made independent of the system input signal but that statistical independence of the error and the input signals is not achievable. Similarly, it is demonstrated that values of the total error signal cannot generally be rendered statistically independent of one another but that their joint moments can be controlled and that, in particular, the error sequence can be rendered spectrally white. The properties of some practical dither signals are explored, and recommendations are made for dithering in audio, video, 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 misunderstandings regarding the technique.