Georgia Institute of Technology


Electrical Engineering

Reproduced with permission from NeXT Computer, Inc.
A Reference Guide to NeXT in Higher Education, Fall 1992
ยช 1992 NeXT Computer, Inc

NeXTSTEP: The platform of choice for signal processing with Mathematica

Brian Evans, a graduate research assistant in the School of Electrical Engineering at Georgia Institute of Technology, has developed packages of Mathematica code and a set of interactive Mathematica Notebooks to supplement lectures and labs in signal-processing and linear systems theory. Evans developed the applications entirely on a NeXT computer, the only workstation that supports Mathematica's Notebook front end.

"The applications are intended to help engineers learn difficult concepts, like piecewise convolution, filter design, and transform theory," says Evans. "Since mathematics underlies much of signal processing, we decided to use a general-purpose computer algebra environment. We chose to work with Mathematica because of its Notebook interface. Students can use the Notebooks as worksheets to solve problems and document solutions. Using the Notebook format, instructors can write interactive tutorials that enable students to discover insights at their own pace. The Notebooks allows them to access material randomly and ask for more information on a subject."

Evans continues, "Most important, though, is the ability to evaluate and tweak existing code as well as to write, edit, and run new code-all while perusing a Notebook. This feature allows students to explore topics, not just read about them, on a computer screen. Mathematica and the NeXT machine go a long way in providing the tools faculty members need to teach signal processing."

However, since Mathematica is geared to mathematical applications, its knowledge of operations and functions common to signal processing is limited. To get around this problem, Evans developed packages to allow Mathematica to understand signals, operators, and transforms common in signal processing. He relied on many of Mathematica's inherent abilities, including symbolic operations of partial-fractions decomposition, series expansion, integration, and differentiation, in creating the signal-processing packages. The packages perform various operations for symbolic, graphic, and numerical analyses of signals and systems, including simplifying expressions and reasoning about properties of signals, as well as plotting magnitude frequency responses and phase frequency responses. Many operations can justify their answers so students can learn to perform the operations themselves.

Many signal-processing Notebooks serve as on-line help for the packages. The Laplace transform Notebook LaPlaceTest, for example, shows how to use forward and inverse Laplace transform rule bases by giving more than 100 examples. The Notebook also includes a section on how to use the linear constant coefficient differential equation solver with LSolve, which relies on Laplace transform rule bases.

One of the Notebooks, PiecewiseConvolution, teaches convolution, a concept basic to both analog and digital signal processing. After showing students how to use PiecewiseConvolution to solve one-dimensional discrete-time and continuous-time convolution problems, the Notebook presents the steps involved in solving such problems by hand. It illustrates this flip-and-slide approach via animation.

Three other Notebooks teach the z-transform, analog filter design, and discrete Fourier analysis. AnalogFilters,the analog filter design Notebook, introduces the topic of filter design and guides the reader through several design examples, including ones for low-pass designs as well as a bandpass, bandstop, and high-pass design. Students use animation to visualize the changes in the filter as they vary the parameters of filter order and/or ripple control; later, they can redesign the filter and observe the results. The z-transform Notebook uses animation to demonstrate the effect that pole and zero locations have on the magnitude response of filters, a basic idea behind digital filter design.

Evans says faculty members at more than a dozen colleges, including the Rose-Hulman Institute of Technology and Stanford University, currently use the applications in their courses.

The signal-processing packages and Notebooks are available via anonymous FTP from gauss.eedsp.gatech.edu (IP #130.207.226.24) as the compressed tar file "SigProc2.0.tar.Z" from the Mathematica directory.

For more information, please contact:

Brian L. Evans
Graduate Research Assistant
School of Electrical Engineering
Georgia Institute of Technology
Atlanta, GA 30332-0250
(404) 894-2910 ext 1
evans@eedsp.gatech.edu