Hypercubes, Kronecker Products & Sorting in Digital Signal Processing

This book covers recent advances and contributions to the area of digital signal processing. It starts with a revisit and a rewriting of the sampling theorem in the context of signals containing discontinuities. The approach of impulse invariance for converting continuous-time domain filters to discrete-time domain filters is questioned in light of the Mittag-Leffler expansion. Higher quality digital filters than those obtained using the present day approach are studied. General base perfect shuffle transformations are shown to be basic operations prevalent in transform factorization and parallel processing. Hypercube transformations, Kronecker products and sorting formalism have had a major impact on transformations of generalized spectral analysis, processor architecture, optimal parallel, massively parallel processing and parallel sorting. The objective of the present book is to render some of the author’s previously and recently published papers in the domain of digital signal processing and the architecture of parallel digital signal processors into a simpler format for all to read. In the topics covered in this book, matrix formalism is often employed. Hypercubes, the Kronecker product of matrices and matrix operators such as the general base perfect shuffle matrix are powerful mathematical tools that effectively convert sequential information into matrices. Matrix formalism is a powerful mathematical tool. In fact, it may be said that if a picture is worth a thousand words, a matrix is worth a thousand equations.