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:

- Understand the relationship between circuits, signals and systems (EE3, 9a)H
- Perform system modeling of circuits using differential and difference equations, state equations, and block diagrams (EE1,5, 9a)H
- Apply linear differential and difference equation techniques to the analysis of linear systems (EE1,5)H
- 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
- Compute the Laplace transforms of continuous-time signals and its inversions (EE1,5)H
- Perform continuous-time system analysis using the Laplace transform and its properties (EE1, 3, 5)H
- Compute Z transforms of discrete-time signals and its inversions (EE1,5)H
- Perform discrete-time system analysis using the Z transform and its properties (EE1,3, 5)H
- Compute the Fourier transforms and series for continuous- and discrete-time signals (EE1, 5)H.
- Perform continuous- and discrete-time signal analysis using the Fourier transforms and series (EE1, 3, 5)H.
- Understand the relationships between time and frequency responses of the transfer functions (EE1,3, 5)H
- Compute the poles and zeros of LTI systems and its effects on the system responses, stability and invertibility (EE1,3, 5)H.
- Apply block diagram techniques to the analysis and synthesis of systems that are described by linear differential and difference equations (EE1, 3, 5)H
- 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:

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