Fundamentals of Signal Processing in Generalized Metric Spaces

Exploring the interrelations between generalized metric spaces, lattice-ordered groups, and order statistics, the book contains a new algebraic approach to Signal Processing Theory. It describes mathematical concepts and results important in the development, analysis, and optimization of signal processing algorithms intended for various applications. The book offers a solution of large-scale Signal Processing Theory problems of increasing both signal processing efficiency under prior uncertainty conditions and signal processing rate that is provided by multiplication-free signal processing algorithms based on lattice-ordered group operations. From simple basic relationships to computer simulation, the text covers a wide range of new mathematical techniques essential for understanding the proposed signal processing algorithms developed for solving the following problems: signal parameter and spectral estimation, signal filtering, detection, classification, and resolution; array signal processing; demultiplexing and demodulation in multi-channel communication systems and multi-station networks; wavelet analysis of 1D/ 2D signals. Along with discussing mathematical aspects, each chapter presents examples illustrating operation of signal processing algorithms developed for various applications. The book helps readers understand relations between known classic and obtained results as well as recent research trends in Signal Processing Theory and its applications, providing all necessary mathematical background concerning lattice-ordered groups to prepare readers for independent work in the marked directions including more advanced research and development.

Andrey Popoff is presently is a leading researcher of EW department at Central Research Institute of Armament and Defence Technologies, Kiev, Ukraine. 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). 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.

1. Introduction to Signal Processing on L-groups. 2. Estimation of Signal Parameters in Sample Spaces with L-group. Properties. 3. Signal Filtering Algorithms in Spaces with L-group Properties. 4. Signal Detection, Classification, and Resolution in Spaces with L-group. Properties. 5. Spectral estimation and Spectral analysis on L-groups. 6. Antenna Array Signal Processing Based on L-group Operations. 7. Signal Processing L-group Algorithms for Communication Systems and Networks. 8. Wavelets on L-groups.