Justification of white noise model for round-off errors in digital systems with fixed point arithmetic

Round-off noise in digital realizations of linear systems in arithmetic with fixed point origins from the following sources: overflow, coefficients quantization, input signal quantization and arithmetic errors. Round-off errors of the two last types are assumed to be independent random vectors in the frames of the uniform white noise model. In this paper, the strict validation is given for full model of uniform white noise in the sense of poor convergence of probabilistic measures in tending of mesh step to zero.