On quantization of noisy signals

Quantized noise distributions derived from continuous signals with additive noise are studied. Two noise sources are considered, quantized image noise derived from the continuous input noise source and noise due to quantization roundoff error. These are 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 excellent agreement in the region of overlapping validity. Quantized noise variance is related to the continuous noise variance from normally distributed noise using these expressions. A table and plots of useful values are 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