Symbolic representation and manipulation of signals

This paper discusses the symbolic representation and manipulation of signals and signal processing operations in computers. Symbolic representation and manipulation of signals, in contrast to numerical representation and manipulation, is the manipulation of signal properties and signal descriptions, rather than the computation of signal values. We identify three classes of symbolic manipulations of signals - symbolic manipulation of signal properties, rearrangement of signal processing expressions, and manipulation of abstract signal classes - and we describe the Extended Signal Processing Language and Interactive Computing Environment (E-SPLICE), a system for the symbolic manipulation of signals. Examples of the symbolic manipulation of signals are given, including expression simplification, generation of equivalent forms of an expression, the manipulation of signal properties, the measurement of computational cost, and the selection of signal processing algorithm implementation.