Geodesic
Noise model of quantization of the vector with non-zero mathematical expectations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 12 (2020) no. 2, pp. 37-48

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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.
Keywords: Fourier series expansion, Fourier integral, normal distribution density with non-zero mathematical expectations resulting in quantization noise. 
@article{VYURM_2020_12_2_a4,
     author = {V. V. Zavolokin},
     title = {Noise model of quantization of the vector with non-zero mathematical expectations},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {37--48},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2020_12_2_a4/}
}
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V. V. Zavolokin. Noise model of quantization of the vector with non-zero mathematical expectations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 12 (2020) no. 2, pp. 37-48. http://geodesic.mathdoc.fr/item/VYURM_2020_12_2_a4/