Myoung An Knihy

Focusing on the intersection of time-frequency analysis and abelian group theory, this work emphasizes the unifying role of group structures in developing theory and algorithms. It is divided into two parts: one covering Weyl-Heisenberg representations over finite abelian groups, and the other addressing multirate filter structures over free abelian groups of finite rank. The methods employed are dimensionless and coordinate-free, facilitating applications to both one and multidimensional problems, while prioritizing simplicity over mathematical necessity.

Application areas covered include pulse radars and sonars, multibeam radar and sonar imaging systems, remote dielectric material identification, and code division multiple-access communication systems. This is an excellent reference text for graduate students, researchers, and engineers in radar, sonar, and communication systems.

This graduate-level text provides a language for understanding, unifying, and implementing a wide variety of algorithms for digital signal processing - in particular, to provide rules and procedures that can simplify or even automate the task of writing code for the newest parallel and vector machines.

Multidimensional Fourier transforms are essential for analyzing large data sets in various fields, including seismology and medical imaging. This book presents algorithms designed for efficient computation on vector and parallel computers, addressing the challenges of multidimensional data processing. It highlights the similarities and differences between one-dimensional and multidimensional transforms, providing insights into optimization strategies. Aimed at applied mathematicians, computer scientists, and professionals in related fields, it covers topics like tensor products, finite Abelian groups, and specific algorithms for implementation.