Quantization is a highly nonlinear process and is very difficult to analyze precisely. Approximations and assumptions are made to make analysis tractable.
Assumption #1
The roundoff or truncation errors at any point in a system at each time are random, stationary, and statistically independent (white and independent of all other quantizers in a system).
That is, the error autocorrelation function is
In this case, rounding has zero mean and variance
Please note that the independence assumption may be very
bad (for example, when quantizing a sinusoid with an integer
period
Assumption #2
Pretend that the quantization error is really additive Gaussian noise with the same mean and variance as the uniform quantizer. That is, model
