A reasonably extensive characterization of the structures of various communication systems using generalized Laguerre functions is presented. Emphasis is placed on the analytical properties of these functions coupled with modern numerical techniques. Three aspects are presented: (1) the development of the most general form of Laguerre functions (all parameters nonintegral and complex) for the purposes of insight into related structures and of suggestions for future investigations; (2) the compilation and interpretation of recent work on interpolation, correlation analyzers, causal functions, a form of the causal central limit theorem, identification of continuous and discrete systems in parametric and nonparametric forms, and the characterization of modes in optical fibers; (3) the presentation of new results in mean-square approximations to functions belonging to L2(O,∞) using Laguerre functions of non-zero order.
