Wolfram Library Archive

All Collections Articles Books Conference Proceedings
Courseware Demos MathSource Technical Notes

Signals and Systems

Mariusz Jankowski
Organization: University of Southern Maine
Department: Electrical Engineering
Education level


The course is to provide a modern introductory coverage of a traditional electrical engineering course on signals and systems. The main objective is to help second- and third-year engineering students acquire the essential skills, both intuitive and formal, to prepare them for the study of such disciplines as signal processing, communication and control. Specifically, students will learn the formal mathematical representations and methods of analysis of LTI systems, will gain a physical and intuitive understanding of the subject and the experience the practice of implementing signal processing algorithms and data manipulation on a computer.

  • Signals and Systems by Allen V. Oppenheim, S. Willsky, with S. Hamid Navab (Prentice Hall, 2nd Edition, 1996)
  • Signals and Systems Made Ridiculously Simple by Zoher Karu (ZiZi Press, 1995)
  • Signals and Systems by Hsu, Schaum's Outline Series (McGraw Hill, 1995)
  • The Mathematica Book by Stephen Wolfram (Cambridge University Press and Wolfram Media, Third Edition, 1996)

Introduction to the theory of linear signals and systems. Analysis of continuous-time and discrete-time signals and systems. Linear, time-invariant (LTI) system properties and representations; differential and difference equations, convolution, Fourier analysis, Laplace and Z transforms. Selected topics in sampling, filter design, discrete signal processing and modulation. Lecture/Laboratory 5 hrs, 4 credits.

Modern mathematical computing systems such as Mathematica have the potential to improve the learning and teaching environments in many science and engineering disciplines. By significantly increasing the use of such powerful visualization and computing tools in the engineering program, I hope to improve levels of understanding of basic concepts, increase student interest, and stimulate active participation

Signals and Systems:
  • basic continuous and discrete-time signals
  • elementary complex signals
  • periodic signals
  • generalized functions
  • fundamental properties of LTI system
Linear Time-Invariant Systems:
  • convolution sum and integral
  • difference and differential equations
Fourier Analysis of Signals and Systems:
  • CT and DT Fourier series
  • CT and DT Fourier transform
  • frequency response of CT and DT LTI systems
Application to Filters:
  • time and frequency characterization of filters
  • introduction to analog and digital (FIR) filter design
Application to Sampling:
  • sampling theorem
  • time- and frequency-domain analysis of sampling
  • interpolation and decimation of discrete-time signals
Application to Modulation
  • Laplace and z-transforms
Special topic:
  • Introduction to time-frequency analysis
  • spectrogram

*Engineering > Electrical Engineering
*Engineering > Signal Processing