DOI: https://doi.org/10.3103/S0735272709050045
Open Access Open Access  Restricted Access Subscription Access

Characteristics and properties of signals space built on generalized Boolean algebra with measure

Andrey A. Popov

Abstract


The characteristics of an arbitrary pair of random processes, which are invariant with respect to the group of random process transformations, are considered. By applying an apparatus of Boolean algebra with measure to the introduced characteristics of random processes, a notion of metric signals space with axiomatic introduction of information quantity measure, which allows to estimate information ratios between random signals and their instantaneous values, is formulated.


Full Text:

PDF

References


V. А. Kotel’nikov, Theory of Potential Interference Immunity (Gostekhizdat, Moscow, 1956) [in Russian].

L. Frenks, Theory of Signals (Prentice-Hall, New Jersey, 1969).

R. Hartley, “Transmission of information,” in Information Theory and Its Applications (Collection of translations) (GI FML, Moscow, 1959) [in Russian, ed. by А. А. Harkevich], pp. 5–35.

C. Shannon, “Mathematical communications theory,” in Works on Information Theory and Cybernetics (Izdat. Inostr. Lit., Moscow, 1963) [in Russian], pp. 243–332.

N. Winner, Cybernetics or Management and Communications in Animal and Machine, 2nd ed. (Sov. Radio, Moscow, 1968) [in Russian].

А.А. Popov, “Invariants of One-to-One Functional Transformation of Random Processes,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 50(11), 35 (2007) [Radioelectron. Commun. Syst. 50(11), 609 (2007)].

J. C. Oxtoby, Measure and Category (Springer, New York, 1971; Mir, Moscow, 1974).

V. А. Artamonov, V. N. Saliy, L. А. Skornyakov, et al., General Algebra, Vol. 1 (Nauka, Moscow, 1991) [in Russian, ed. by L. А. Skornyakov].

D. A. Vladimirov, Boolean Algebras (Nauka, Moscow, 1969) [in Russian].

R. Sikorskiy, Boolean Algebras (Mir, Moscow, 1969) [in Russian].

V. А. Artamonov, V. N. Saliy, L. А. Skornyakov, et al., General Algebra, Vol. 2 (Nauka, Moscow, 1991) [in Russian, ed. by L. А. Skornyakov].

A. N. Kolmogorov, Basics of the Probability Theory, 2nd ed. (Nauka, Moscow, 1974) [in Russian].







© Radioelectronics and Communications Systems, 2004–2020
When you copy an active link to the material is required
ISSN 1934-8061 (Online), ISSN 0735-2727 (Print)
tel./fax +38044 204-82-31, 204-90-41