ELE314: Signals and Systems

Department of Electrical Engineering
University of Southern Maine

Instructor: Mariusz Jankowski
Office: 127 John Mitchell Center
Telephone: (207) 780-5580
E-mail: mjankowski@usm.maine.edu


Course Description: Introduction to the theory of linear signals and systems. Analysis of continuous-time and discrete-time signals and systems. Linear, time-invariant (LTI) system properties and representations; differential and difference equations, convolution, Fourier analysis, Laplace and Z transforms. Selected topics in sampling, filter design, discrete signal processing and modulation. Lecture 3 hrs, Laboratory 2 hrs. Credits 4. Prerequisites: ELE211, MAT350, COS160 or equivalent.

Course Objectives:
- To understand the fundamental characteristics of LTI continuous-time and discrete-time systems and their effect on signals.
- To be familiar with time- and frequency-domain representations of LTI systems and to understand the inter-relationships between the two domains.
- To understand the principles of sampling, filtering and modulation.
- To develop the mathematical skills to analyze signals and systems using the Fourier, z and Laplace transforms.

Course Outcomes:
1. Students should be able to determine the output of a linear, time invariant system to an arbitrary input using the convolution sum
2. Students should be able to solve constant-coefficient difference and differential equations
3. Students should be able to calculate the impulse response of a discrete-time system
4. Students should be able to compute the Fourier series expansion of periodic signals
5. Students should be able to compute the Fourier transform of non-periodic signals.
6. Students should be able to analyze the effect of frequency selective filters on input signals using frequency domain analysis.
7. Students should be able to design simple FIR filters
8. Students should be able to determine the sampling rate, and to evaluate the effect of aliasing
9. Students should be able to compute and display the spectrogram of a signal.

Laboratories: This course is part of the "Integrating Mathematica into the electrical engineering curriculum" project. Included are a series of Mathematica notebooks. Students will be expected to use Mathematica to solve problems in class, as well as in take-home assignments and projects.

Textbook: "Signals and Systems, " Simon Haykin and Barry Van Veen, Wiley, 2nd Edition.

Lecture Topics Reading Homework Problems
1-3 Signals and Systems - basic continuous and discrete-time signals, elementary complex signals, periodic signals, singularity functions, fundamental properties of LTI systems. 1.1-1.8 5-9, 11, 13, 17, 42, 43, 46, 48, 50, 54, 56, 60, 77
4-7 Linear Time-Invariant Systems - convolution sum and integral, difference and differential equations 2.1-12 32, 33, 38, 41, 49, 50, 52, 57, 59
8-11 Fourier Analysis of Signals and Systems - response of LTI systems to complex exponentials, CT and DT Fourier series 3.1-5 48(b,c,d), 49(b,c,e), 50(a,d,f), 51(a,d,e), 64(b,c), 97
12-15 Fourier Analysis of Signals and Systems - CT and DT Fourier transform, frequency response of CT and DT LTI systems 3.6-18 3: 52(b,c,f), 53(a,c,f), 54(a,d,f), 55(a,d,f), 56, 57, 63(a,c), 66(a,d), 68, 69(a,c), 70(a,d), 71, 72, 77

4: 16(a,d), 17(a,c), 18(a), 22(a,b)

16-18 Applications - sampling 4.1-6 4: 24(a,b,c), 25, 26, 29(b,d)
19-21 Applications - communications 5.1-10 5: 17, 18(a,b,d), 20, 28, 30, 31
22-25 LTI system as frequency selective filter, time and frequency characterization of filters, introduction to filter design 8.1-12 8: 16
26-27 Laplace and z-transforms 6, 7  


Grading policy: The final grade will be based on the results of 7 mid-semester quizzes (each 30 minutes), a final exam and computer projects. These will be weighted equally, each part contributing approximately a third of your final grade.

 

Academic Support for Students with Disabilities - If you need course adaptations or accommodations because of a disability please contact the Office of Academic Support for Students with Disabilities, 237 Luther Bonney Hall, 780-4706, TTY 780-4395.