Digital Signal Processing by Atomic Functions and Wavelets

The monograph is devoted to research and development of methods for analysis of physical systems based on theories of R- and atomic functions, WA-systems of functions, the construction of processing algorithms, and simulation of remote sensing and radio astronomy processes with the objective of improving the physical characteristics of the transmission, recovery, and recognition of multidimensional signals. The new weight functions (windows) and finite impulse response filters based on them, as well as analytical and orthogonal wavelets are described. The generalized sampling theorem based on atomic functions and its special cases are studied. The algorithm of synthesis of multidimensional functions with a reference area of the complex shape geometry is developed. The generalization of the ambiguity function of time and frequency in relation to the analysis of complex sounding signals is proposed and substantiated. The book is intended for researchers, postgraduates, and students working in the field of digital signal processing as applied to current problems of radio physics and radioengineering.