Subtractive and Nonsubtractive Dithering: A Mathematical Comparison

A comparative analysis of subtractively and nonsubtractively dithered quantizing systems, with and without noise-shaping error feedback, is presented. A review of the principal results prefaces the most thoroughgoing mathematical analysis of either system that currently exists in print. The relative advantages and disadvantages of each system are compared, addressing their inherent signal-to-noise ratios and the requirement for knowledge of the dither signal at the receiver in subtractive systems. It is shown that subtractively dithered systems can render the total error statistically independent of the input signal at the expense of requiring knowledge of the dither signal at the receiver. On the other hand, nonsubtractively dithered systems can at best render specified statistical moments of the total error independent of the input and will introduce greater total noise into the output, although they do not require knowledge of the dither signal at the receiver. The treatment extends to include new findings regarding signal correlations in subtractively and nonsubtractively dithered systems, and regarding subtractively dithered systems using spectrally colored dither signals and/or noise-shaping error feedback. The new results are proven as needed for purposes of comparison.