Linear Discrete-Space Systems and Undergraduate Education

The cornerstone of the theory of discrete-space linear systems is the idea that every such system has an input-output map H that can be represented by a convolution sum or the familiar generalization of a convolution sum. This thinking involves an oversight which, for the case of bounded inputs mapped continuously into bounded outputs, was recently corrected by adding an additional term to the representation. Here we give a necessary and sufficient condition under which the additional term vanishes. The condition provides the basis for some related material given concerning engineering education and introductory courses in the area of signals and systems. Key-Words: linear systems, multidimensional systems, shift-varying systems, myopic maps.