Catalog Entry (2012-2013):

3550 Signals and Linear Systems(3) Continuous and discrete time representations of signals. System modeling and analysis using differential and difference equations. Fourier, Laplace and z transforms. State description of continuous and discrete time transfer functions. The primary mathematical tools used in the analysis of continuous and discrete time systems. Prereq: CEEN 2140; Pre or Coreq.: STAT 3800.

Text:

S. Haykin and B. Van Veen, Signals and Systems, Wiley 1999.

Class/Laboratory Schedule:

Three university hours for lecture per week.

Course Outcomes:

The students who successfully complete this course will be able to:

  1. Understand the relationship between circuits, signals and systems (EE3, 9a)H
  2. Perform system modeling of circuits using differential and difference equations, state equations, and block diagrams (EE1,5, 9a)H
  3. Apply linear differential and difference equation techniques to the analysis of linear systems (EE1,5)H
  4. Understand the fundamental concepts of continuous- and discrete-time signals and systems such as linear time-invariant, convolution; impulse, step and exponential responses; stability, causality (EE3)H
  5. Compute the Laplace transforms of continuous-time signals and its inversions (EE1,5)H
  6. Perform continuous-time system analysis using the Laplace transform and its properties (EE1, 3, 5)H
  7. Compute Z transforms of discrete-time signals and its inversions (EE1,5)H
  8. Perform discrete-time system analysis using the Z transform and its properties (EE1,3, 5)H
  9. Compute the Fourier transforms and series for continuous- and discrete-time signals (EE1, 5)H.
  10. Perform continuous- and discrete-time signal analysis using the Fourier transforms and series (EE1, 3, 5)H.
  11. Understand the relationships between time and frequency responses of the transfer functions (EE1,3, 5)H
  12. Compute the poles and zeros of LTI systems and its effects on the system responses, stability and invertibility (EE1,3, 5)H.
  13. Apply block diagram techniques to the analysis and synthesis of systems that are described by linear differential and difference equations (EE1, 3, 5)H
  14. Apply the computational and mathematical tools to solve practical engineering problems, using a system approach, in modern communications and signal processing systems (EE3)H, (EE4, 9f)M.

Course Topics:

  1. Review of dynamic time equations and solutions for electrical circuits. 1 week
  2. Continuous and discrete-time signal and system concepts: linear time-invariant (LTI) systems, convolution, exponential, impulse and step responses. 3 weeks
  3. Signal analysis with Fourier transforms and series 2 weeks
  4. Frequency response of LTI systems with Fourier transforms 1.5 weeks
  5. Laplace transform: properties and system analysis 2 weeks
  6. Z-transform: properties and system analysis 1.5 weeks
  7. System modeling and analysis using differential and difference equations, state variables and block diagrams 2 weeks
  8. Applications: samplings, communications systems, signal processing 2 week

The Reason this Course is in the Program:

The objective of this course is to introduce the students the fundamentals and applications of continuous and discrete-time signals and systems. The time-dynamic equations and solutions of electrical circuits are employed to motivate the basic concepts in signals and systems. The course emphasis is on continuous and discrete-time representation of signals, system modeling and analysis using differential and difference equations, state variables and block diagrams. Mathematical tools of Laplace, Fourier and z transforms are studied in details. The goal is to develop the student ability for solving practical engineering problems, using a system approach, in modern communication and signal processing systems.

Prepared by:

Lim Nguyen - August 20, 2002