Symbolic z-transforms using DSP knowledge bases

The implementation of basic signal analysis and transforms for DSP (digital signal processing) with a symbolic mathematical program called Mathematica is described. By extending its capabilities through a proper representation of knowledge of discrete signals, operators, and transforms, Mathematica can take the forward and inverse z-transforms symbolically and apply the discrete Fourier transform (DFT) as a symbolic summation. In addition to the 150+ common mathematical operators and functions built into Mathematica, the rule-based package defines 23 systems and 8 basic signals. Six of these systems provide the ability to take forward and inverse z-transforms, DFTs, and DTFTs of multidimensional signal processing expressions. More importantly, this package allows the user to manipulate signals (functions or data) and systems (operators) as algebraic expressions. The user can convert symbolic signal processing expressions to graphical, numeric, and textual representations