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.
1. Basic electrical circuit laws
2. Complex variables
3. Differential equations
4. Linear algebra
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.
- 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|
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
Homework problems are not graded, but the exams are based on homework. Students discuss homework solutions with the instructor during office hours.