Digital Non-Subtractive Dither: Necessary and Sufficient Condition for Unbiasedness, with Implementation Issues

Dither theory gives the condition of unbiasedness for non-subtractive dither, which can only be fulfilled with continuous-amplitude dithers. However, within a computer or a DSP, only digital dither can be used. A condition was given for digital dither, however, the condition and the proof was only approximate. This paper makes the statement precise, and gives a full proof for unbiasedness. Implementation issues are also discussed