Hypercubes, Kronecker Products and Sorting in Digital Signal Processing

The area of Digital Signal Processing DSP has received a particular attention in recent years. From a revisit of the sampling theorem in light of the Mittag-Leffler expansion with a considerable impact on conversion of continuous-domain to digital filter design, to Hypercube transformation, to Kronecker product formalism, to transforms of generalized spectral analysis to processor architecture to parallel processing, it has had a major impact on many scientific domains and electrical and electronic designs and implementations.

Graduate level textbooks and monographs on DSP usually deal with theoretical aspects of signal processing and are often described in advanced level, condensed, and often complex published papers. The objective of the present book is to render easier reading 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, through added details and examples. In some of 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 Permutation Matrix and in particular the General Base Perfect Shuffle matrix, are powerful mathematical tools that effectively allow us to convert sequential information into two-dimensional data appearing as images. If an image is worth a thousand words, a matrix is worth a thousand equations.