DOI
10.34229/KCA2522-9664.26.1.3
UDC 621.396
I. Pitukh
West Ukrainian National University, Ternopil, Ukraine,
pirom75@ukr.net
ALGORITHMIC FOUNDATIONS OF MODULAR ARITHMETIC DETERMINATION
OF SAMPLE MATHEMATICAL EXPECTATION
Abstract. The mathematical foundations and algorithms for determining the sample expectation of stationary random processes are investigated. The functional limitations of the algorithms for determining the sample expectation in binary arithmetic of the Rademacher number-theoretic basis are substantiated. The low speed of determining the sample expectation in the Rademacher number-theoretic basis codes is due to the presence of end-to-end transfers when performing operations for accumulating the sums of the input digitized data of the random process. Lattice models and graphs of rank sum formation during the streaming accumulation of digital data on the sampling interval of a random process are presented. The theoretical foundations for algorithms determining the sample expectation in a non-positional number system of the Haar–Crestenson number-theoretic basis of residues are developed. Recommendations for choosing Haar–Crestenson code modules that correspond to four-bit codes of the Rademacher basis and eight-bit codes of RGB pixels of color images are provided. The results of the study allow expanding the functionality and increasing the speed of statistical data processing at the lower levels of interactive distributed computer systems.
Keywords: digitized sensor data, residual class system, Rademacher, Haar, and Haar–Krestenson numerical theoretical bases, special processor architectures, RGB pixel codes.
full text
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