Characteristics and properties of signals space built on generalized Boolean algebra with measure
DOI:
https://doi.org/10.3103/S0735272709050045Abstract
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.
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].