EE235
Name:
Student ID:
Final Exam
University of Washington EE235, Winter 2016
March 14th, 2016
Exam Information:
The test is closed book, and no calculators/devices are allowed. You are allowed ONE 8.5x11 (twosided) page of notes.
Please show all work.
EE 235, Winter 2016, Homework 5: More LTI Systems
Due Friday February 5, 2016 via Canvas Submission
Write down ALL steps for full credit
HW5 Topics:
Impulse Response and Step Response
LTI System Properties
Exponential Response
HW5 Course Learning Goals
EE 235, Winter 2016, Homework 5 Supplementary Notes
1. Magnitude and Phase for a Ratio of Complex Numbers.
Consider X = X1
X2 , where X1 and X2 are complex.
(a) Evaluating Magnitude. We can evaluate the magnitude of X by taking the magnitude of the
numera
EE 235, Winter 2016, Homework 7 Supplementary Notes
1. Partial Fraction Expansion. When the order of the numerator is greater than or equal to the order of
the denominator, you must perform a polynomial division first before doing a partial fraction expan
EE 235, Winter 2016, Homework 7: Fourier Transforms
Due Friday February 19, 2016 in class
Write down ALL steps for full credit
HW7 Topics:
Fourier Transforms: Analyze (Transform) and Synthesize (Inverse Transform)
Fourier Transforms: Periodic Signals
P
EE 235, Winter 2016, Homework 1 Supplementary Notes
1. Complex Number Representation. Any complex number z can be represented in rectangular (Cartesian)
form or in polar form.
(a) In rectangular form, z = x + jy, where x = Recfw_z and y = Imcfw_z .
i. Com
EE 235, Winter 2016, Homework 6 Supplementary Notes
1. For Problems 1a: Partial Fraction Expansion. This week, we will only consider the case where we have
complex roots in the denominator or possibly repeated roots, but with the order of the numerator st
EE235
Name:
Student ID:
Midterm Exam #1
University of Washington EE235, Winter 2016
January 29th, 2016
Exam Information:
The test is closed book, and no calculators/devices are allowed. You are allowed ONE 8.5x11 (twosided) page of notes.
Please show al
EE 235, Winter 2016, Homework 6: Fourier Series
Due Friday February 12, 2016 via Canvas Submission
Write down ALL steps for full credit
HW6 Topics:
Fourier Series: Analysis, Synthesis, Properties, and LTI
HW6 Course Learning Goals Satisfied:
Goal 1: Des
EE 235, Winter 2016, Homework 10 Supplementary Notes
LAPLACE TRANSFORM PROPERTIES:
PROPERTY
LAPLACE TRANSFORM
ROC
A x1 (t) + B x2 (t)
A X1 (s) + B X2 (s)
ROC = at least ROC1 ROC2
x(t to )
esto X(s)
ROC = ROCx
x(t), > 0
1
s
X( )
ROC = ROCx
x(t)
X(s)
ROC =
EE 235, Winter 2016, Homework 9: Sampling and Modulation
(Due Friday March 4, 2016 in class)
Write down ALL steps for full credit
HW9 Topics:
Sampling Theorem and Aliasing
Modulation and Demodulation
HW9 Course Learning Goals Satisfied:
Goal 5: Underst
EE 235, Winter 2016, Homework 8: Fourier Transforms, LTI Systems, and Filters Due
Wednesday February 24, 2016 in class via Canvas Submission
Write down ALL steps for full credit
HW8 Topics:
Fourier Transforms: LTI
LTI Filters
HW8 Course Learning Goals S
EE 235, Winter 2016, Homework 10: Laplace Transforms
Due Friday March 11, 2016 via Canvas Submission
Write down ALL steps for full credit
HW10 Topics:
Laplace Transform and Inverse Laplace Transform
Laplace Transform ROC and Signal Properties
Laplace T
7/6/2015
EE 341:DISCRETE TIME LINEAR SIGNALS
AND SYSTEMS
LECTURE #8
UW EE TC Chen
PERIODICITY PROPERTIES OF DISCRETE-TIME
COMPLEX EXPONENTIALS
Any discrete-time periodic sequence [] is complete
specified by a finite number .
There is no convergence issu
7/7/2015
EE 341:DISCRETE TIME LINEAR SIGNALS
AND SYSTEMS
LECTURE #9
UW EE TC Chen
DETERMINING MEMORY
Memoryless: The output depends only on
the current value of the input
If [] = [] depends only on []
UW EE TC Chen
1
7/7/2015
MEMORY EXAMPLES
Examples: tes
6/29/2015
EE 341:Discrete time signals and
systems
Lecture #5
UW EE TC Chen
SIGNAL TRANSFORMATION
Example: How about z = [2/3]
Now speed up first, = [2]
[]
[]
[]
0
[0]
2
1
[1]
0
2
[2]
2
3
[3]
0
-1
[1]
0
UW EE TC Chen
1
6/29/2015
SIGNAL TRANSFORMATION
Exam
6/24/2015
EE 341:Discrete time signals and
systems
Lecture #3
UW EE TC Chen
Energy and Power signals
All physical activity is mediated by a
transfer of energy. No real physical
system can response to an excitation
unless it has energy.
UW EE TC Chen
1
6/2
7/8/2015
EE 341:DISCRETE TIME LINEAR SIGNALS
AND SYSTEMS
LECTURE #10
UW EE TC Chen
TEST TIME INVARIANCE
Example 1: test if the system is time-invariant.
Given = [2]
1. Find 0
0 = [2 0 ]
2. Find 0
0 = [2 0 ]
3. Compare, it is NOT TI
UW EE TC Chen
1
7/8/2
7/1/2015
EE 341:Discrete time signals and
systems
Lecture #7
UW EE TC Chen
EVEN AND ODD SIGNALS
Every signal sum of an odd and even signal.
1
1
= + [] + []
2
2
The even and odd parts of a signal
1
= + []
2
1
= []
2
And
0 = 0
0 = 0
UW EE TC Chen
1
7/1
6/30/2015
EE 341:Discrete time signals and
systems
Lecture #6
UW EE TC Chen
DISCRETE TIME PERIODIC FUNCTIONS
Periodic signals are defined analogously in discrete time.
Specifically, a discrete time signal [] is periodic with period
, where is a positive i
6/23/2015
EE 341:DISCRETE TIME LINEAR SYSTEMS
LECTURE #2 (1.1 SIGNALS AND ENERGY,
POWER,
UW EE TC Chen
SIGNALS AND SYSTEMS DEFINED
A signal is any physical phenomenon which conveys
information
Systems respond to signals and produce new signals
Excitati
4/20/2016
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #15
UWEE TC Chen
LTI SYSTEMS WITH AND WITHOUT
MEMORY
Memory: An LTI system is memoryless iff () is a scaled
(unshifted) Dirac.
= ()
UWEE TC Chen
1
4/20/2016
INVER
3/9/16
EE235: Lecture 26
LCCDE and the LT
Interconnected LTI Systems
Pole-Zero Plots
Eect of zeros
1
LCCDE & LT: Example #1
Given the DE: y'(t) + 3y(t) = x(t)
Find H(s), ROC, and h(t).
LT both sides to get algebraic expression:
s
3/11/16
EE235: Lecture 27
Course Review
EE235 Topics
Signal
x(t)
a x1(t)+ b x2(t)
x(t-t0)
x(t)
Eigenfunction
est
Fourier Series
ckejk0t
System
Output
y(t)
LTI
a y1(t)+b y2(t)
y(t-t0)
h(t)
Convolution
x(t) * h(t)
h(t)
h(t)
Time
domain
H(s) est
H(jk0) ck
4/27/2016
EE235: Continuous time linear systems
Introduction to signals and systems
Lecture #17
UWEE TC Chen
ZERO-STATE OUTPUT OF LTI SYSTEM
Total response(t)=Zero-input response (t)+Zero-state
output(t)
Response to our input x(t)
LTI system: characteri
2/17/16
EE235: Lecture 19
Linear Phase LTI Systems
LTI Filters
An application of the FT to analyze systems
1
Frequency Response of LTI Systems
()
H ( j ) =
LTI
()() = Y()
Y ( j )
= | H ( j ) | H ( j )
X( j )
Note: |H(j0)| for =0 is the DC gain
|H(j)| is
2/24/16
EE235: Lecture 21
Amplitude Modulation
Demodulation for sinusoidal AM
Frequency-division multiplexing
An application of the FT to analyze systems
f (t)g(t)
1
F( j ) *G( j )
2
1
Communication Systems
All wireless communication transmits data t