ECEN 3300, Linear Systems, Fall 2009

ECEN 3300 - Linear Systems

Peter Mathys, Fall 2009

Course Description and Requirements

Class: MWF 3-3:50 pm, ECCR 1B55
- Lab (Section 011): MW 9-10:50 am, ECEE 281A, Call #: 74069
- Lab (Section 012): MW 12-1:50 pm, ECEE 281A, Call #: 74070
- Lab (Section 013): MW 5:30-7:20 pm, ECEE 281A, Call #: 74071
Instructor: Professor Peter Mathys, ECOT 334, 303-492-7733, Fax: 303-492-2758, e-mail: .
Office Hours: M,W 10-12, T,R 11-1, F 12-2, and by appointment.
TAs:
- Kaniska Mohanty, e-mail: .
- Darren Anderson, e-mail: .

Text: Alan V. Oppenheim, Alan S. Willsky, with S. Hamid Nawab, Signals & Systems, Second Edition, Prentice Hall, 1997, ISBN 0-13-814757-4, and additional notes by instructor.

Prerequisites:
- APPM 2360, Intro to Linear Algebra and Differential Equations
- ECEN 2260, Circuits/Electronics 2
Credit Hours: 5

Description: The concepts of signals and systems are abstractions that allow engineers and scientists to describe, analyze, synthesize and simulate a wide variety of naturally occuring and man-made processes within a common, implementation-independent framework. In traditional electrical engineering systems often originate from circuits consisting of lumped elements and/or active integrated circuits. In this case the signals are usually time-varying voltages and currents associated with the inputs and outputs of the circuit. Modern system implementations, on the other hand, increasingly rely on fast computer hardware to perform signal processing in the digital domain. In this case the input and output signals take on the form of discrete-time (DT) sequences that are often obtained by sampling continuous-time (CT) waveforms at regular time intervals. The digital systems or digital signal processors themselves generally consist of memory cells, adders, and multipliers.
Of central importance are linear and time-invariant (LTI) systems, i.e., systems which satisfy the superposition principle and whose properties are independent of absolute time. Together with Fourier analysis, which models most physical signals or sequences of interest as linear combinations of spectral components, this leads to a "divide and conquer" approach for the analysis and synthesis of a large class of practically relevant processes. Examples include linear circuits, filters, and general signal and information processing that is used in communication systems, image processing systems, and linear feedback systems.

Concepts Covered:
1. Introduction: CT and DT signals and LTI systems
2. Circuits to CT Systems: 1'st and 2'nd order CT circuits, Laplace transform, N-th order CT systems, CT system function, CT unit impulse response, lowpass to highpass and bandpass transformations, highpass to bandstop transformation
3. CT to DT Systems: 1'st and 2'nd order DT circuits, z-transform, N-th order DT systems, DT system function, DT unit impulse response, impulse invariant and bilinear CT to DT system transformation
4. Convolution, Generalized Functions: CT and DT convolution, definition of unit impulse and its properties, causality, stability
5. Fourier Transform (FT): Properties of FT, basic FT pairs
6. Discrete-Time Fourier Transform (DTFT): Properties of DTFT, basic DTFT pairs
7. Sampling Theorem: Nyquist frequency, aliasing, sampling, interpolation
8. Fourier Series (FS): Properties of FS, basic FS pairs, FT-FS relationship
9. Discrete Fourier Transform (DFT): Properties of DFT, basic DFT pairs, FT-DTFT-DFT relationship, fast Fourier transform (FFT)
10. Linear Feedback Systems: Negative feedback, stabilization of unstable systems, root-locus analysis, Nyquist stability criterion
11. Applications: Filters, communications, phase-locked loops (PLL)
The following figure shows how the main topics of this course are related to each other.

Computer Usage: All computer lab descriptions, homework, and course notes will be posted on the class website at http://ecee.colorado.edu/~mathys/ecen3300. The computer labs will require the use of Matlab. Some of the labs will also require Simulink, and some experiments will use the sound card of the computer and speakers or headphones.

Course Requirements:
1. Attend class.
2. Homework (~10%): Weekly, usually due on Fridays at the beginning of class. Only one problem (or the equivalent of one problem), selected at random, will be graded.
3. Recitation (~5%): Weekly, first lab hour on Wednesdays. Used to solve recitation problem sets and discuss problems related to homework and labs.
4. Computer Labs (~20%): Weekly Mon. and Wed., lab report is usually due at the beginning of the next lab.
5. Quizzes (~15%): Approximately weekly, on material covered in class and/or labs.
6. Exam 1 (~15%): Wed. Oct. 7. Closed book, closed notes.
7. Exam 2 (~15%): Wed. Nov. 18. Closed book, closed notes.
8. Final exam (~20%), according to final exam schedule: Wed. Dec. 16, 7:30 - 10:00 pm. Closed book, closed notes.

Format for Lab Reports: Lab reports consist of two parts as follows:
- Part 1 (Group effort, one submitted per group)
  1. Brief statement of the goals of the lab
  2. Chronological description of lab work (for E1,E2,...)
    - How the experiment was set up, schematics, computations needed for setup
    - How the experiment was run, conditions, any special observations
    - The results that the experiment produced (raw data, labeled graphs, etc), any problems that were observed that could affect the validity of the results
- Part 2 (Individual effort, one submitted per student)
  1. Discussion of results
    - Any outcomes and observations from the experiments that you found to be surprising or unexpected, or which triggered "what if" questions, etc.
    - Answers to specific lab questions
  2. Conclusion
    - Do theory and practice agree? If so, under what conditions? If not, why not?
    - What were the most important concepts that you learnt and/or reinforced in this lab?
    - What were the most interesting aspects of this lab?
    - How could the experiments be improved to achieve the goals of the lab?
- Each group needs to maintain a lab notebook where notes, measurement data, designs, analysis, etc. are recorded. This provides the "raw data" for much of part 1 of the lab report.

Course Goals: Learn how to describe, analyze, and design linear and time-invariant continuous-time (CT) and discrete-time (DT) systems for signal and information processing. Describe CT and DT signals and systems in the time and frequency domains. Simulate CT and DT processes in Matlab and Simulink. Develop a balanced analytical and intuitive understanding of linear systems that allows you to analyze and solve a wide variety of engineering problems.