ECEN3300  Linear Systems
Lectures: MWF 2:002:50 ECCR 245
Instructor: Kelvin Wagner
Office:
ECEE 232 (inside Optics Center)
email:
kelvin@colorado.edu
phone:
3034924661
Office
hours: Th 4:305:30 PM and by appointments
Lectures: Monday, Wednesday and Friday 2:002:50pm in ECCR 245
 Text: Alan V. Oppenheim, Alan S.
Willsky, with S. Hamid Nawab, Signals & Systems,
Second Edition, Prentice Hall, 1997, ISBN 0138147574.
 Prerequisites:
 APPM 2360, Intro to Linear Algebra and Differential
Equations
 ECEN 2260, Circuits/Electronics 2 (min grade C)
 Credit Hours:3
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
manmade processes within a common, implementationindependent
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 timevarying
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 discretetime (DT) sequences that are often obtained by
sampling continuoustime (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 timeinvariant (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.
 (1) Continuous time (CT) signals;
 (2) CT linear and timeinvariant (LTI) systems: Linearity,
timeinvariance, memory, causality, Block diagrams;
 (3) Time domain analysis of CT LTI systems: Differential
equations,Unit impulse/step response, Convolution;
 (4) Frequency domain analysis of CT LTI systems: Laplace
transform, pole/zero plots, Fourier transform, System function and
frequency response;
 (5) Discrete time (DT) signals;
 (6) DT linear and timeinvariant (LTI) systems:Linearity,
timeinvariance, memory, causality, Block diagrams;
 (7) Time domain analysis of DT LTI systems: Difference
equations, Unit impulse/step response, Convolution;
 (8) Frequency domain analysis of DT LTI systems:
ztransform, pole/zero plots, DT Fourier transform, discrete Fourier
series, System function and frequency response
 (9) Relationship between CT and DT signals and systems.
Course Goals: Learn how to describe, understand,
analyze, and design linear and timeinvariant continuoustime (CT) and
discretetime (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 Ztransform.
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 
MagnitudePhase 

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 
Ztransform 

Inverse Ztransform 

LTI system characterization using Ztransform 

04/30/18 

05/02/18 

05/04/18 
15 
Block Diagrams 

Linear Feedback Systems 

Nyquist Criteria 



05/09/18 





Final 1:304:00 


Exams
Entrance quiz
The entrance quiz will be given in
class on Monday January 22, 2018. This will be counted as part of the
1012% quiz score towards your grade. The quiz will consist of two problems
chosen from the following topics:

operations on complex numbers,

CIrcuits represented with differential equations, transfer functions
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, 1:30PM4:00 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
 Computer Usage: All
homework and course notes will be posted on the class
website at
http://ecee.colorado.edu/~ecen3300. Some homework will
require the use of Matlab.
 Course Requirements:
 Attend class.
 Homework (~30%): Weekly, usually due
on Fridays at the beginning of class. Only one or two problem, selected at random, will be graded.
 Quizzes (~10%): Approximately biweekly,
on material covered in class and in the book.
 Exam 1 (~15%): Mon. Feb 19. Closed
book, closed notes. Transform tables provided when needed.
 Exam 2 (~15%): Fri. Mar 23. Closed
book, closed notes. Transform tables provided when needed.
 Final exam (~30%): Wed. May 9, 1:30PM  4:00 pm. Closed book,
closed notes. Transform tables will be provided.
Homework, Labs, and Grades
Nominal due dates
Guidelines for getting
full credit on Homework

Assignments must be neat,
organized and legible.
In plain English: If we cannot read your assignment, you will not get
credit for it.
Typed assignments are welcome.

At the start of each problem,
write out a brief description of the problem including given
information and what is to be found.

Show your work enough to fully
demonstrate your understating and your arrival at your answer.

Write on only one side of the
paper.

Pages must stapled be in order
(i.e. following the order in which the problems were assigned).

Unless otherwise stated,
plots must be computergenerated (in MATLAB, Excel, etc.)

All plots must have a title and
each axis should be labeled. Do not forget units.

Put a box around all final
answers.

If coding is used in a problem,
you must turn in a paper copy of your computer code along with your
assignment. Attach the code immediately after each problem that
required code.

Computer code should be clearly
commented to demonstrate your intent.

You should go over your homework
as soon as it has been graded and returned to you.

Once an assignment has been
returned to you, you only have TWO WEEKS from the return date to
question the grading. Questions regarding the material are always
welcome.
External links:
Linear Systems Tutorials
Matlab Tutorials
Complex Numbers Tutorial Websites:
top
January 6 2018 KW