## 14: 332: 345 – Linear Systems and Signals

Course Catalog Description:

14: 332: 345 – Linear Systems and Signals (3)
Introduction to continuous- and discrete-time systems and signals, basis function representation of signals, convolution, Fourier Series, Fourier, Laplace, Z-transform theory, state space variable analysis of linear systems, basic feedback concepts.

Pre-Requisite Courses:

14:332:222

Co-Requisite Courses:

14:332:347 Linear Systems Lab

Pre-Requisite by Topic:

1. Basic electrical circuit laws
2. Complex variables
3. Differential equations
4. Linear algebra

Textbook & Materials:

Z. Gajic, Linear Dynamic Systems and Signals, Prentice-Hall, 2003.

References:

H. Hsu, Signals and Systems, McGraw Hill’s Schaum Series, 1995

Overall Educational Objective:

To develop skills to analyze linear dynamic systems in both continuous- and discrete-time, find the system response in both time and frequency domains, and examine system stability. To understand the use of the Fourier, Laplace, and Z transforms in analysis of signals and systems.

Course Learning Outcomes:

A student who successfully fulfils the course requirements will have demonstrated:
- an ability to recognize, use, and analyze signals coming from diverse disciplines and represent them in
terms of elementary signals such as step, ramp, parabolic, sinusoidal, and exponential signals.
- an ability to understand basic signals operations such as convolution, correlation, signal shifting.
- knowledge and understanding of linear system dynamics.
- knowledge of methods for finding the system transient and steady state responses.
- understanding of basic linear dynamic systems concepts such as stability, observability and controllability.
- ability to represent and study linear systems in the state space form and build corresponding system block diagrams.
- knowledge of main properties of linear feedback systems.
- full understanding of Fourier, Laplace, and Z transforms and their inverses.

How Course Outcomes are Assessed:

• Quizzes (10%)
• Three in-class exams (55%)
• Final exam (35%)

N = none S = Supportive H = highly related

Outcome Level Proficiency assessed by
(a) an ability to apply knowledge of Mathematics, science, and engineering H Quizzes, Exams
(b) an ability to design and conduct experiments and interpret data N
(c) an ability to design a system, component or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability S
(d) an ability to function as part of a multi-disciplinary team N
(e) an ability to identify, formulate, and solve ECE problems H Exams
(f) an understanding of professional and ethical responsibility N
(g) an ability to communicate in written and oral form H Quizzes, exams
(h) the broad education necessary to understand the impact of electrical and computer engineering solutions in a global, economic, environmental, and societal contex N
(i) a recognition of the need for, and an ability to engage in life-long learning S Discussions during lectures
(j) a knowledge of contemporary issues N
(k) an ability to use the techniques, skills, and modern engineering tools necessary for electrical and computer engineering practice H Exams
Basic disciplines in Electrical Engineering H Quizzes, Exams
Depth in Electrical Engineering H Quizzes, Exams
Basic disciplines in Computer Engineering S MATLAB Simulations
Depth in Computer Engineering N
Laboratory equipment and software tools S MATLAB
Variety of instruction formats S Lecture, office hour discussions

Topics Covered week by week:

Week 1: Mathematical background; Time vs. Frequency domains; Common signals and delta impulse function
Week 2: Fourier series
Week 3: Fourier transform and its properties
Week 4: Fourier transform of common signals
Week 5: Laplace transform and its properties
Week 6: The inverse Laplace transform; Applications of the Laplace Transform
Week 7: The z-transform and its properties
Week 8: Continuous-time linear systems; Discrete-time linear systems
Week 9: Convolution of continuous- and discrete-time signals
Week 10: Impulse and step system responses
Week 11: State space representation of continuous-time systems
Week 12: State space representation of discrete-time systems
Week 13: Stability of continuous- and discrete-time systems
Week 14: System controllability, observability, and basic feedback concepts
Week 15: Review and Final Examination

Computer Usage:

MATLAB is used to demonstrate linear systems concepts and methods. MATLAB is also required for the corresponding linear system and signals laboratory.

Laboratory Experiences:

See description for course 332:347 Linear Systems and Signals Laboratory, which is associated with this course.

Design Experiences:

The course is mostly analytical. However, students get some exposure to the design of transfer functions, block diagrams, and elementary feedback systems using MATLAB and Simulink.

Independent Learning Experiences :

Homework problems are assigned weekly with the solutions posted on the class website a week after.
Homework problems are not graded, but the exams are based on homework. Students discuss homework solutions with the instructor during office hours.

Contribution to the Professional Component:

(a) College level mathematics and basic sciences: 0.5 credit hours.
(b) Engineering Topics (Science and/or Design): 2.5 credit hours
(c) General Education: 0 credit hours
Total credits: 3

Prepared by:
Z. Gajic
Date:
May, 2011