Multivariate Polynomial Fundamentals for Multidimensional Systems

The subject of multidimensional systems is concerned with a mathematical framework for tackling a broad range of paradigms whose analysis or synthesis require the use of functions and polynomials in several complex variables. Its applications, which may range from the processing of spatial and temporal signals of diverse physical origin to the design of linear discrete multidimensional control systems, are already plentiful. The areas of image processing, linear multipass processes, iterative learning control systems, lumped-distributed network synthesis, nonlinear system analysis via multidimensional transforms and geophysical signal processing have benefited from the tools available in the theory of multidimensional systems [2, 6]. Progress towards the use of the theory in problems of very recent origin like multidimensional convolutional coding for communications has been increasing at a rate which is becoming increasingly difficult to track because of the wildly scattered nature of the voluminous publications by researchers from several disciplines, who are contributing to this area. This book aims to promote interaction between a broad spectrum of scientists and engineers so that not only are theoretical results developed to their fullest possible extent but also clear exposition and interpretation are provided for these results to become useful to practitioners in distinct but related disciplines. The presentation is intended to be concise but complete.