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Methods of presentation and imitation of discrete random signals within the framework of generalized correlation theory

DOI 10.18127/j19997493-201901-03

Keywords:

A.V. Proletarsky – Dr.Sc.(Eng.), Professor, Dean of Faculty, «Informatics and Control Systems», Bauman MSTU
E-mail: pav@bmstu.ru
V.V. Gurenko – Associate Professor, Department «Computer systems and networks», Bauman MSTU
E-mail: wgurenko@bmstu.ru
V.V. Syuzev – Dr.Sc.(Eng.), Professor, Department «Computer systems and networks», Bauman MSTU
E-mail: v.suzev@bmstu.ru
K.A. Neusypin – Dr.Sc.(Eng.), Professor, Department «Automatic Control Systems», Bauman MSTU
E-mail: neusipin@bmstu.ru


The paper presents the theoretical and applied fundamentals of the formation of p stationary pseudo-random signals within the framework of the generalized correlation theory in a one-base number system with an arbitrary base p. They include the original me-thods and algorithms of the canonical and spectral description and simulation of continuous and discrete pseudo-random signals in the Vilenkin–Chrestenson function basis in Hadamard ordering. There was given a method of setting up simulation algorithms for specified energy characteristics.
The results obtained in the work are generalized. At the basis of the numeration system, equal to the number of reference points of the finite discrete simulation interval, and with the single-digit representation code of the number and the argument of the basis function, they coincide with the results of the frequency representation. In the case of a binary number system, the results give a sequential representation of the signals. With other bases of the number system, the considered generalized theory provides new important for the practice algorithms of description and imitation, differing in computational complexity.
It is noted that the transition from the Hadamard system to other ways of streamlining Vilenkin–Chrestenson basis functions leads to results similar to those presented in the article. Thus, the obtained descriptions and algorithms for simulating random signals in the framework of the considered correlation theory are invariant to the method of ordering functions in the Vilenkin–Chrestenson basis.
Further development of the obtained imitation algorithms the authors see in their simplification. In particular, this can be achieved by transition to the basis of real generalized Hartley functions. Unlike the functions of the Vilenkin–Chrestenson basic system, they do not contain complex arithmetic operations, which will allow the implementation of signal simulation algorithms that use only real number operations. This, in turn, will reduce their computational complexity.

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