EE341, Winter 2014
Problem Set #7
Due: 5 March 14
Problem 1 is from the text by Oppenheim, Willsky & Nawab, and problems 2-4 are adapted
from the text by Phillips, Parr & Riskin.
1. 5.55(b)
2. Consider two length-4 discrete time signals:
x[n] = ej
2n
4
h[
EE 341
Discrete-Time Linear Systems Week 10
Spring 2011
A Final Exam Example Problem 1 (Multiple Choice QuestionsCircle the Single Best
Answer and Justify it.)
a) It is desired to build a sampling system which takes a recorded orchestral music signal s (t
Spring 2011
Clark
EE 341
Lab 3: The DFT and Digital Filtering
Due: In your discussion section May 11-13
When using a digital computer, frequency analysis and filtering requires that we use
the Discrete Fourier Transform (DFT). In this lab we spend some ti
Spring 2011
EE 341
Lab 1
Lab 1: Elementary Music Synthesis
Due: In your discussion section 4/13 (Sec. AA and Sec. AD), 4/14 (Sec. AB),
or 4/15 (Sec. AC). The hard copy report is to be turned in to your TA just
before the above discussion begins. In additi
EE341, Winter 2014
HW #1 Solutions
Due: 15 January 14
1. A discrete-time signal is shown in Figure P1.22. Sketch and label carefully each of the
following signals:
Figure P1.22
(d) x[3n + 1]
(e) x[n]u[3 n]
(f) x[n 2][n 2]
Solution
(d) Since x[n] is non-ze
EE 341
Spring 2010
Prof. Atlas
Final Exam
June 9, 2010
Your Name:
Solutions
Exam Instructions:
1. Open book and notes. But as listed in our course syllabus: No turned-on
electronic devices (calculators, laptops, ipods, cell phones, beepers, etc.)
are allo
EE 341
Spring 2009
Prof. Atlas
Final Exam
June 10, 2009
Your Name:
Solutions
Exam Instructions:
1. Open book and notes. But as listed in our course syllabus: No electronic
devices (calculators, laptops, netbooks, PDAs, cell phones, beepers, etc.)
are allo
Ghost HW
Selected Solutions
Edited List of Problems
The problems about difference
equations have been omitted
here. They will show up for
REALS on the next assignment
2.21
2.28
2.41
2.51
Thats it!
HW 1 Solutions
Problem 1
Problem 2
pi/2
pi
pi/2
5pi/6
-5pi/6
Problem 3
Problem 4
Note: there were 2 different figures
Problem 4:
results for Initial Figure
the initial figure included in HW 1 Problem 4
Problem 4: Initial Figure
Problem 4: Initial Figure
P
EE 341
August 2011
Discrete Time Linear Systems
HW 9 - Ghost
Sampling
1. 7.22
Z transforms
2. 10.21 b, c, f, h
3. 10.22 a, c. Express all sums in closed form.
4. 10.26
5. 10.30
Note: Good additional practice for the nal: 10.24, 10.32. 10.34
EE 341
Autumn 2011
Discrete Time Linear Systems
HW 3
As always, your answer is incorrect unless you explain clearly how you arrived at it. I
expect answers to be a combination of graphs/sketches/mathematics and language.
1. For each of the systems, determ
EE341, Spring 2014
HW #7 Solutions (for parts 1-4)
Due: 28 May 14
1. (From textbook 5.55 (b)
Solution
(b) From (P5.55-1) we can write
M
[n k]
w[n] =
k=M
From Table 5.2 and given X(ej ) we have
x[n] =
sin(n/4)
n
Now p[n] = w[n]x[n] can be written as
M
p[n]
HW 3
Solutions
Problem 1
(1), (2), (3), (4) Inverse system
(1), (3), (4), (5)
(4), (5)
(1), (3), (4)
Inverse system
(2), (3), (4), (5)
(2), (5) Inverse system
(1), (2), (3), (4), (5)
Inverse system
Problem 2
Solution
Problem 2
The book says: The series in
HW 6 Solutions
Autumn 2011
EE 341
Problem 1: P3.27
This problem is sort of flawed. We decided to ignore the
nonzero piece, and assume that the info they give us
truly does specify all 5 unique DFS coefficients.
Problem 2: P3.28 a
Solutions
6
1X
kn
ak =
x[
HW 7 Solutions
Autumn 2011
EE341
Problem 1
Problem 1
Problem 1
Here we can plot in some context of normalized frequency in
order to analyze. In the case of X1[k], k is from 0 to 3, so w =
2*pi*k/N where N is 4 tells us that each of those values
belongs at
HW 4
Solutions
Problem 1
a)yes
b)no
c)no
d)yes
e)yes
f)no
g)no
Problem 2
We notice that
If the system is Linear and Time Invariant, then
This is NOT true, however, so the system cannot be LTI. Since
we were told that it is linear, it must not be TI.
Probl
HW 8 Solutions
EE341
Autumn 2011
Problem 1
Design fft algorithm for DFT length 4: I chose
Decimation in time radix 2, like in class.
SOLUTION
Let the 4 point DFT of x[n] be defined as X[k], and we note that:
X[k] =
3
X
kn
x[n]W4
n=0
We can first try and b
HW 2 Solutions
EE 341 Autumn 2011
Problem 1
Part a)
Part a)
Alternatively, could use Method 1
Part b)
Part c)
Part c)
Alternatively could use Method 1
Part d)
Problem 2
Part a)
And for xo[n]
Part b)
Part c)
Part d)
Part e)
Problem 3
Problem 4: Book 1.26
P
EE 341
Summer 2011
Discrete Time Linear Systems
Midterm
Your Name:
Exam Instructions:
1. Open book and notes. No electronic devices (calculators, laptops, ipods, cell phones,
etc.)
Please turn all devices o now.
2. Do not open the exam until 1:10.
3. Jus
EE 341
Autumn 2011
Discrete Time Linear Systems
HW 2
1. Let x[n] = n(u[n + 2] u[n 4]). Find and plot the following signals utilizing Method
1 or Method 2 for the time axis transformations as discussed in class. Draw a block
diagram describing your order o
EE 341
Autumn 2011
Discrete Time Linear Systems
HW 1
1. Write these complex numbers in their cartesian form: x + yj where x, y are real. Plot
your results in the complex plane.
(a)
(b)
(c)
(d)
(e)
3
2ej 2
1
2 ej9
5
jej 2
2
1
(1 + 2j)( 2 + j)
2/(1 + j)
2.
Name
ID Number
Section
Final EE341
20 March 2014
Instructions:
The test is closed book and you are allowed two 8.511 page of notes. No calculators are allowed.
Show all work. Partial credit will be given for partial work; NO credit will be given for no
Final Exam Formula Sheet
E341 Discrete-Time Linear Systems
Complex numbers and sinusoids: (j = 1)
1
1
cos() = (ej + ej )
sin() = (ej ej )
2
2j
rej = r cos() + jr sin()
cos( + ) = cos() cos() sin() sin()
Summation formulas
X
an
for |a| < 1, n 0
ak =
1a
k=n
EE341 Midterm Solutons Winter 2016
Mean = 74
1. (20 points)
For each of the statements below, say whether each is true or false, and explain your reasoning.
(a) The two signals below are the same:
x1 [n] = 1 + ejn
x2 [n] =
X
[n 2k]
k=
Solution: FALSE
(
n
Question 1
Sunday, March 13, 2016
12:03 AM
Homework 8 Page 1
Sunday, March 13, 2016
12:03 AM
Homework 8 Page 2
Sunday, March 13, 2016
12:03 AM
Since this system is right sided, the region of convergence is
outside the largest pole which is 0.89. This mean