Symbolic Transforms with Applications to Signal Processing

Volume 1, Issue 2
Fall 1990

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.

The packages can perform a variety of operations for symbolic, graphical and numerical operations of signals and systems. Symbolic analyses include simplification of expressions, determination of data types, and reasoning about properties of signals, such as stability. Plotting capabilities include discrete time-domain plots, magnitude and phase frequency responses, and plot-zero diagrams, including the region of convergence, for z- and Laplace transforms.