ECEN3300 - Linear Systems


Lectures: MWF 2:00-2:50 ECCR 245

Instructor: Kelvin Wagner

    Office: ECEE 232 (inside Optics Center)
    e-mail: kelvin@colorado.edu
    phone: 303-492-4661
    Office hours: Th 4:30-5:30 PM and by appointments
    Lectures: Monday, Wednesday and Friday 2:00-2:50pm in ECCR 245

Topics

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 diverse topics including optics and imaging, RF/electromagnetics, antennas, acoustics, linear circuits, filters, and general signal and information processing that is used in communication systems, radar and lidar, optics and image processing systems, acoustics, quantum mechanics, linear feedback systems, robotics and controls.
Course Goals: Learn how to describe, understand, 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. Understand the utility of the various transform domains including Fourier Series, Fourier Transfoirms, Discrete Time Fourier Transforms, Laplace transforms, and the Z-transform. Be able to simulate, evaluate, and analyze CT and DT processes in Matlab. Develop a balanced analytical and intuitive understanding of linear systems that allows you to analyze and solve a wide variety of engineering problems.

Homework




Quizes


Tentative Schedule


Monday
Wednesday
Friday

01/15/18
01/17/18
01/19/18
1 MLK Holiday
Complex Numbes
Signals

01/22/18
01/24/18
01/26/18
2 Entrance Quiz and Signal Properties
Intro to Systems
System properties

01/29/18
01/31/18
02/02/18
3 LTI DT convolutions
LTI CT convolutions
Block Diagrams and Differential Equations

02/05/18
02/07/18
02/09/18
4 Difference Equations
Differential Equations
Impulse Response

02/12/18
02/14/18
02/16/18
5 FS
FS
FS

02/19/18
02/21/18
02/23/18
6 Midterm 1
FT
FT

02/26/18
02/28/18
03/02/18
7 FT
FT
FT

03/05/18
03/07/18
03/09/18
8 DTFT
DTFT
DTFT

03/12/18
03/14/18
03/16/18
9 Magnitude-Phase
Bode Plots
CT

03/19/18
03/21/18
03/23/18
10 DTFT
Sampling
Midterm 2

03/26/18
03/28/18
03/30/18

Spring Break
Spring Break
Spring Break

04/02/18
04/04/18
04/06/18
11 Sampling Theorem
Aliasing
Communication Systems

04/09/18
04/11/18
04/13/18
12 Unilateral and Bilateral Laplace Transforms
ROC and Inverse Laplace Transform
Laplace Transform Properties

04/16/18
04/18/18
04/20/18
13 Partial Fraction Expansion and Examples
LTI System Characterization using Laplace Transforms
Block Diagrams and Differential Equations

04/23/18
04/25/18
04/27/18
14 Z-transform
Inverse Z-transform
LTI system characterization using Z-transform

04/30/18
05/02/18
05/04/18
15 Block Diagrams
Linear Feedback Systems
Nyquist Criteria



05/09/18




Final 1:30-4:00



Exams

Entrance quiz

The entrance quiz will be given in class on Monday January 22, 2018. This will be counted as part of the 10-12% quiz score towards your grade. The quiz will consist of two problems chosen from the following topics:

Previous entrance exam solutions.   Previous entrance exam and solutions part1,  part2.
Another previous Entrance exam and solutions

Midterms

The first midterm will be on or about Feebruary 19. The midterm will count for 15% of your grade. Practice Exams that are representative of the type of midterm, but with different problems

Midterm from previous year  -- solutions
Practice Midterm1  -- brief solns
Midterm 1 solutions

The second midterm will take place on March 23. The midterm will count for 15% of your grade.

Practice Midterm 2 -- soln
Midterm 2 solutions

Final

The final exam will take place on Wednesday May 9, 1:30PM-4:00 PM. The final will include all the topics covered in class during the semester for which homework has been assigned and will count towards 30% of your grade.

Practice Final -- Practice Final Solutions

Grading



Homework, Labs, and Grades

Nominal due dates

Guidelines for getting full credit on Homework


External links:

Linear Systems Tutorials

Matlab Tutorials

 Complex Numbers Tutorial Websites:



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January 6 2018 KW