DITHERED QUANTIZERS

Dithered quantization is a technique in which a signal called a dither is added to an input signal prior to quantization. This purposeful di stortion of an input signal is common, because it can result in a more subjectively pleasing reproduction and because, under certain conditi ons, it can cause the quantization error to behave in a statistically nice fashion. In particular, suitably chosen random dither signals can cause the quantization error to be signal independent, uniformly dist ributed white noise. Unfortunately, however, these properties do not i n general imply similar properties for the overall quantization noise in many systems, and this has caused some confusion in the understandi ng, application, and interpretation of the basic results. A theory of overall quantization noise for nonsubtractive dither was originally de veloped in unpublished work by Wright and by Stockham and subsequently expanded by Brinton, Lipshitz, Vanderkooy, and Wannamaker. These resu lts are not as well known as the original results, however, and misund erstanding persists in the literature. New proofs of the aforementione d properties of quantizer dither, both subtractive and nonsubtractive are provided. The new proofs are based on elementary Fourier series an d Rice's characteristic function method and do not require the traditi onal use of generalized functions (impulse trains of Dirac delta funct ions) and sampling theorem arguments. The goal is to provide a unified derivation and presentation of the two forms of dithered quantizer no ise based on elementary Fourier techniques.