1st Edition
Fundamentals of Signal Processing in Metric Spaces with Lattice Properties Algebraic Approach
Exploring the interrelation between information theory and signal processing theory, the book contains a new algebraic approach to signal processing theory. Readers will learn this new approach to constructing the unified mathematical fundamentals of both information theory and signal processing theory in addition to new methods of evaluating quality indices of signal processing. The book discusses the methodology of synthesis and analysis of signal processing algorithms providing qualitative increase of signal processing efficiency under parametric and nonparametric prior uncertainty conditions. Examples are included throughout the book to further emphasize new material.
1 General Ideas of Natural Science, Signal Theory, and Information Theory
1.1 General System of Notions and Principles of Modern Research Methodology
1.2 Information Theory and Natural Sciences
1.3 Overcoming Logical Difficulties
2 Information Carrier Space Built upon Generalized Boolean Algebra with a Measure
2.1 Information Carrier Space
2.2 Geometrical Properties of Metric Space Built upon Generalized Boolean Algebra
2.3 Informational Properties of Information Carrier Space
3 Informational Characteristics and Properties of Stochastic Processes
3.1 Normalized Function of Statistical Interrelationship of Stochastic Processes
3.2 Normalized Measure of Statistical Interrelationship of Stochastic Processes
3.3 Probabilistic Measure of Statistical Interrelationship of Stochastic Processes
3.4 Information Distribution Density of Stochastic Processes
3.5 Informational Characteristics and Properties of Stochastic Processes
4 Signal Spaces with Lattice Properties
4.1 Physical and Informational Signal Spaces
4.2 Homomorphic Mappings in Signal Space Built upon Generalized Boolean Algebra
4.3 Features of Signal Interaction in Signal Spaces with Various Algebraic Properties
4.4 Metric and Informational Relationships between Signals Interacting in Signal Space
5 Communication Channel Capacity
5.1 Information Quantity Carried by Discrete and Continuous Signals
5.2 Capacity of Noiseless Communication Channels
6 Quality Indices of Signal Processing in Metric Spaces with L-group Properties
6.1 Formulation of Main Signal Processing Problems
6.2 Quality Indices of Signal Filtering in Metric Spaces with L-group Properties
6.3 Quality Indices of Unknown Nonrandom Parameter Estimation
6.4 Quality Indices of Classification and Detection of Deterministic Signals
6.5 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 Properties
6.7 Quality Indices of Signal Resolution-Estimation in Metric Spaces with Lattice Properties
7 Synthesis and Analysis of Signal Processing Algorithms
7.1 Signal Spaces with Lattice Properties
7.2 Estimation of Unknown Nonrandom Parameter in Sample Space with Lattice Properties
7.3 Extraction of Stochastic Signal in the Presence of Interference (Noise)
7.4 Signal Detection in Metric Space with Lattice Properties
7.5 Classification of Deterministic Signals in Metric Space with Lattice Properties
7.6 Resolution of Radio Frequency Pulses in Metric Space with Lattice Properties
7.7 Methods of Mapping of Signal Spaces into Signal Space with Lattice Properties
Conclusion
Bibliography
Index
Biography
Andrey Popoff received a Specialist degree (an intermediate one between B.S. and M.S.) in electronic systems from Kiev Radioengineering Institute of Air Defence in 1985 (in Kiev, former USSR). He started his career as an officer of Electronic Intelligence Corps in the Central group of troops of USSR Armed Forces deployed in former Czechoslovakia (now Czech Republic).
A. Popoff received his Candidate of Science degree (Ph.D. equivalent) in electronic systems/defence technologies from Kiev Military Institute of Control and Communication in 1996. As an instructor at Kiev Military Institute of Control and Communication, and later as an assistant professor, associate professor, professor at National Academy (later renamed to National University) of Defence of Ukraine, A. Popoff worked in the fields of Electronic Warfare (EW), information theory, signal processing, radar and communication systems, and also led courses on the corresponding topics. At present, A. Popoff is a retired colonel and research professor of EW research laboratory at Central Research Institute of Armament and Defence Technologies, Kiev, Ukraine.
