Noise model of quantization of the vector with non-zero mathematical expectations

The mathematical model of quantization noise arising in high-precision measuring systems is obtained. A new formula of the probability distribution density is obtained for the quantization algorithm with rounding to the nearest whole normal vector with non-zero mathematical expectations. This formula is a generalization of the result obtained for the probability density of the echo signal from drops of atmospheric moisture. The formula is obtained on the basis of the probability theory, Fourier series expansions and Fourier integral. For this density, the formulas of the expectation vectors and the second initial moment are obtained.