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

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.

14:332:347 Linear Systems Lab

1. Basic electrical circuit laws

2. Complex variables

3. Differential equations

4. Linear algebra

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

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

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.

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

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

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

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.

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.

(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