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Symbolic Transforms with Applications to Signal Processing

Brian L. Evans
Organization: University of Texas
Department: Department of Electrical and Computer Engineering
URL: http://www.ece.utexas.edu/~bevans/
James H. McClellan
Organization: Georgia Tech
Wallace B. McClure
Organization: Georgia Institute of Technology
Journal / Anthology

The Mathematica Journal
Year: 1990
Volume: 1
Issue: 2
Page range: 70-80

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, determinations 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 pole-zero diagrams, including the region of convergence, for z- and Laplace transforms.

*Engineering > Signal Processing