User's Guide to the Signal Processing Packages and Notebooks for Implementing Linear System Theory in Mathematica 1.2 and 2.0

We describe a hierarchical set of packages to perform basic analyses of signals (functions) and systems (operators). The packages are based on transform theory, and implement a general mechanism for encoding knowledge about transforms, so their applicability extends beyond signal processing to any field where transform analysis is needed. We support (bilateral) z- and Laplace transforms, as well as continuous-time, discrete-time, and discrete Fourier transforms, all in arbitrary dimension. These rule bases can fully justify their answers. When they cannot find a particular transform, users have the choice of either specifying the missing transform pair(s) or letting the transform apply its definition using built-in Mathematica operations. The packages can perform a variety of symbolic, graphical, and numerical operations on signals and systems. In symbolic terms, the packages can solve linear constantcoefficient difference and differential equations by using the z and Laplace transform..