Fundamentals of Signal Processing in Metric Spaces with Lattice Properties: Algebraic Approach

Content: 1 General Ideas of Natural Science, Signal Theory, and Information Theory1.1 General System of Notions and Principles of Modern Research Methodology1.2 Information Theory and Natural Sciences1.3 Overcoming Logical Difficulties2 Information Carrier Space Built upon Generalized Boolean Algebra with a Measure2.1 Information Carrier Space2.2 Geometrical Properties of Metric Space Built upon Generalized Boolean Algebra2.3 Informational Properties of Information Carrier Space3 Informational Characteristics and Properties of Stochastic Processes3.1 Normalized Function of Statistical Interrelationship of Stochastic Processes3.2 Normalized Measure of Statistical Interrelationship of Stochastic Processes3.3 Probabilistic Measure of Statistical Interrelationship of Stochastic Processes3.4 Information Distribution Density of Stochastic Processes3.5 Informational Characteristics and Properties of Stochastic Processes4 Signal Spaces with Lattice Properties4.1 Physical and Informational Signal Spaces4.2 Homomorphic Mappings in Signal Space Built upon Generalized Boolean Algebra4.3 Features of Signal Interaction in Signal Spaces with Various Algebraic Properties4.4 Metric and Informational Relationships between Signals Interacting in Signal Space5 Communication Channel Capacity5.1 Information Quantity Carried by Discrete and Continuous Signals5.2 Capacity of Noiseless Communication Channels6 Quality Indices of Signal Processing in Metric Spaces with L-group Properties6.1 Formulation of Main Signal Processing Problems6.2 Quality Indices of Signal Filtering in Metric Spaces with L-group Properties6.3 Quality Indices of Unknown Nonrandom Parameter Estimation6.4 Quality Indices of Classification and Detection of Deterministic Signals6.5 Capacity of Communication Channels Operating in the Presence of Interference (Noise)6.6 Quality Indices of Signal Resolution-Detection in Metric Spaces with L-group Properties6.7 Quality Indices of Signal Resolution-Estimation in Metric Spaces with Lattice Properties7 Synthesis and Analysis of Signal Processing Algorithms7.1 Signal Spaces with Lattice Properties7.2 Estimation of Unknown Nonrandom Parameter in Sample Space with Lattice Properties7.3 Extraction of Stochastic Signal in the Presence of Interference (Noise)7.4 Signal Detection in Metric Space with Lattice Properties7.5 Classification of Deterministic Signals in Metric Space with Lattice Properties7.6 Resolution of Radio Frequency Pulses in Metric Space with Lattice Properties7.7 Methods of Mapping of Signal Spaces into Signal Space with Lattice PropertiesConclusionBibliographyIndex