Signals and Systems Pack
On October 2, 1995, Wolfram Research Inc.
(1-800-441-MATH) released the Signals and Systems Pack.
The initial release of the Signals and Systems Pack contained
version 3.0.1 of the Signal Processing Packages
(released October 2, 1995) which are compatible with versions 2.0, 2.1,
and 2.2 of Mathematica.
The most recent release of the Signals and Systems Pack
is for Mathematica 5.0.
The Signals and Systems Pack extends the symbolic mathematics
environment Mathematica in the following
- Continuous and Discrete Signal Analysis
- Linear Transforms
- Analog and Digital Filter Design
- Symbolic and Multidimensional Operations
Mathematica in Signal Processing
The foundation of signal processing lies in calculus, matrix algebra,
linear operator theory, vector spaces, and number theory.
With signal processing tasks relying so heavily on mathematics,
Mathematica is a natural
environment for work in this area.
Integrated seamlessly with its high-powered numeric and graphical
capabilities are an outstanding collection of robust symbolic functions
for algebraic equation solving, integration, and differentiation.
A core component of signals and systems curricula, symbolic techniques
are fundamental to the understanding of signal processing concepts.
And while traditional software has not taken full advantage of symbolic
techniques, engineers are finding them increasingly useful.
Signals and Systems Pack brings powerful symbolic
computation capabilities to engineers and educators working in these
fields. These essential tools for working with signals and systems from the
signal processing perspective extend the domain of signal processing
software to a wide variety of techniques not traditionally open to the
engineer. For instance, you can use the pack to express and manipulate of
signals of infinite extent, work with analog signals, perform operations on
some nonseparable multidimensional signals, and conduct other system
manipulation tasks. In addition, having the full power of
Mathematica behind the pack enables
you to extend the functionality to cover your particular application.
Essential Functions for Linear Signals and Systems
With the Signals and Systems Pack, you can begin immediately to
analyze signals, design filters, and perform other routine signal processing
Tasks that involve linear transforms, standard signal representations,
and visualization become greatly simplified.
You can also perform algebraic manipulation on signals and systems
to improve, develop, and implement new algorithms.
And Mathematica's high-level
programming language allows you to use the pack as an extensible core for
handling a wide variety of advanced signal processing problems.
Tools in the pack enable engineers to extend their analysis to symbolic
Standard tools such as pole-zero and magnitude-phase plots will
make your job easier.
Sophisticated code is also provided for some special purpose design tasks,
such as the graphical design of two-dimensional resampling systems.
Working with the pack gives you access to the full capabilities
of Mathematica, so you can work with
its unlimited range of numeric and symbolic computation techniques, and
create sophisticated graphics to visualize your ideas and results.
Educators will find the pack particularly useful in designing signals and
systems courseware, as it provides all the standard signal representations.
It enhances these by allowing the user to track the steps taken by most
important routines (such as the transforms) to help students better
understand the techniques used.
You can present interactive lessons--- containing problems and explanations---
in a Mathematica notebook, and
have students derive, explain, and submit their solutions in the same notebook.
In fact, a prototype of the Signals and Systems Pack has been
used successfully to teach college courses around the world.
Engineering students at the Georgia Institute of Technology,
the Rose-Hulman Institute of Technology,
Washington State University,
University of California at Berkeley,
Stanford University, and
many other institutions have all benefited from this technology.
- Signal Representations and Operators
- Sinc Functions
- Dirichlet Sinc Kernel
- Unit Singularity Functions (with step, pulse, and impulse functions
in discrete and continuous time)
- Standard Windowing Functions
- Piecewise Representations of Functions
- Continuous Operators-Shift, Scaling, Rotation, and Others
- Additional Discrete Operators-Upsampling, Downsampling, and Others
- Convolution and Correlation
- Linear Transforms
- Discrete Fourier
- Discrete-time Fourier
- Region of Convergence Tracking for Laplace and Z Transforms
- Transforms Support Bilateral Forms
- Linear difference and differential equations solving
- Filter Design
- Analog Filter Design of Standard Bessel, Butterworth, Chebyshev
Type I and II, and Elliptic Types
- Digital IIR Filters-Bilinear Transform, Impulse Invariance
- Digital FIR Filters-Windowing
- Computation of Standard Filter Parameters
- Analysis Tools
- Special Plots of Signals
- Pole-Zero Plots
- Magnitude-Phase and Bode Plots
- Root-Locus Plots
- Nyquist Plots
- Report Generation Functions (automatically perform transforms and
generate plots for signal analysis)
- Other Capabilities
- Two-dimensional Resampling System Design
- Analysis of Aliasing in Two-dimensional Decimation Systems
- Smith Forms of Resampling Matrices
- Export of System Representations to Ptolemy
The Signals and Systems Pack is available for all platforms that run
Mathematica 2.2 or later.
(Versions that support the notebook front end are required in order to use
The pack is distributed on 3.5" high-density diskettes and includes complete
documentation in the form of a 200-page report.
Signals and Systems Pack diskettes for Unix systems are provided in
Sun SPARC format.
Alternative media are available by special order.
Mathematica Applications Library Developer Series
The Signals and Systems Pack is published by
Wolfram Research Inc. as part of the
Mathematica Applications Library Developer
This series features specialized application packages created by independent
developers with extensive experience in their fields.
Engineers, researchers, scientists, and analysts around the world use
Mathematica every day to do numerical
and symbolic computations, analyze data, and create graphics and animations.
Hundreds of built-in functions for operations like matrix manipulation,
equation solving, differentiation and integration, data analysis, and
two- and three-dimensional graphics make Mathematica a comprehensive and
efficient productivity tool for a wide range of technical projects.
Mathematica's high-level programming language makes it easy to extend the
system for your own customized solutions.
Furthermore, using MathLink you can communicate with your existing C and
The notebook interface makes Mathematica easy to use and ideal for
recording ideas, writing technical reports, putting together technical
presentations, and sharing work electronically with colleagues and clients
across multiple platforms.
Mathematica runs on over 20 computer platforms.
About the Signals and Systems Pack
The Signals and Systems Pack has been developed by
Wolfram Research Inc., in cooperation with
Dr. Brian L. Evans.
It is based on a prototype developed from 1989-1993 by
Brian L. Evans and
Prof. James H. McClellan
at the Georgia Institute of Technology
for Brian Evans' Ph.D. dissertation entitled
A Knowledge-Based Environment for the Design and Analysis
of Multidimensional Multirate Signal Processing Algorithms.
Dr. Evans is presently a tenured Associate Professor at The University
of Texas at Austin.
The packages are copyright © 1989-2001 Georgia Tech Research Corporation.
All other components of the Signals and Systems Pack are
copyright © 1994-2001 Wolfram
This fact sheet was written by Katherine
Csizmadia of Wolfram Research Inc., and modified and converted to
HTML by Brian L. Evans.
Processing Packages -