ON QUANTIZATION OF NOISY SIGNALS

Quantization of noisy signals modifies both signal and noise characteristics. In this paper we study quantized noise distributions derived from continuous signals with additive noise. Two noise sources are considered, quantized noise derived from the continuous input noise source and noise due to quantization roundoff error. These will be treated as statistically independent sources. An analytic solution for the quantized noise probability density is obtained. The analytic solution is estimated by two expressions valid for normally distributed noise over different ranges of variance. The estimates have excelent agreement in the region of overlapping validity. Using these expressions, quantized noise variance is related to the continuous noise variance from normally distributed noise. A table and plots of useful values is included. These results are helpful in choosing a quantization interval for a particular application. They can also be used to determine quantizer output noise level and signal-to-noise ratio in digital applications.