ABSTRACT
deals with the notions of informational and physical signal spaces. On the basis of probabilistic and informational characteristics of the signals and their elements, that are introduced in the previous chapter, we consider the characteristics and the properties of informational signal space built upon generalized Boolean algebra with a measure. At the same time, the separate signal, carrying information, is considered as subalgebra of generalized Boolean algebra with a measure. It is underlined that a measure on Boolean algebra accomplishes twofold function: firstly, it is a measure of information quantity, and secondly, it induces metric in signal space. The interconnection between introduced measure and logarithmic measure of information quantity is shown. Some homomorphic mappings in informational signal space are considered. Particularly, for this signal space, the sampling theorem is formulated. Theorems on isomorphisms are established for informational signal space. The informational paradox of additive signal interaction in linear signal space is considered. Informational relations, taking place under signal interaction in signal spaces with various algebraic properties, are established. It is shown, that from the standpoint of providing minimum losses of information contained in the signals, one should carry out their processing in signal spaces with lattice properties.
