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 areas:

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.

The Mathematica 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 operations. 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 domains. 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.

Features

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
- Laplace
- Fourier
- Z
- 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

Technical Facts

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 on-line documentation.) 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 Series. This series features specialized application packages created by independent developers with extensive experience in their fields.

About Mathematica

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 Fortran routines. 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.

This fact sheet was written by Katherine Csizmadia of Wolfram Research Inc., and modified and converted to HTML by Brian L. Evans.

Signal Processing Packages - Ptolemy Project