ECE601 Linear Systems
Assignment #3
1. Determine the Fourier series representation for the following signals
a) f(t) is periodic with period T=2 and
f(t) =
t
e
for - 1 t 1
b) f(t) is periodic with period T=4 and
cfw_
f (t)= sin t 0 t 2
02 t 4
2. Let
f (t)
Random signl analysis I (ECE673)
Solution assignment 6
1. Two independent discrete random variables X1 and X2 are known to have the following
marginal PMF:
1/2 k = 1
pXi (k ) =
i = 1, 2.
1/2 k = 2
(i ) Evaluate the joint PMF of X1 and X2 : pX1 ,X2 [k1 , k
. Random Slgnal Analysis I, Ending 2011
mnfnmy distributed between -1/2 and 1! 2i
Praia-lam 2. Lat X and Ybe twn random variablss with juint IDF fmyhr) and juint CDF itiu
Fxmix, y)- Let Z = mama, Y) . Find the PDF on ifX and Far: independent. _
Prahlem 3.
Random signl analysis I (ECE673)
Assignment 9
1) Consider the random process dened as
X [n] = 2U [n] 4U [n 1],
where U [n] is a white noise with zero mean and variance 2 = 1.
(i ) Is this process WSS? If so, evalutate, auto-correlation sequence (see previ
Random signal analysis I (ECE673)
Solution assignment 4
1. If Y = 2X + 1, where X is a Poisson random variable with = 5, nd the set of possible
values for Y (SY ) and the expression of the probability mass function of Y (pY [yi ]): Moreover,
evaluate the
ECE 673-Random signal analysis I
Test 1 - Oct. 4, 2006
Please write legibly and provide detailed answers.
We are interested in studying the connectivity of M towns along a country road (see gure,
where M = 4). Because of unreliable weather conditions, the
ECE 673-Random signal analysis I
Test 2 - Nov. 29, 2006
Please write legibly and provide detailed answers.
You are given an IID process U [n] with probability mass function (PMF)
1/2 u = 1/2
pU [u] = P [U [n] = u] =
.
1/2 u = 2
(i ) Consider the process X
Department of Electrical & Computer Engineering
New Jersey Institute of Technology
ECE 673: Random Signal Analysis
March 23, 2015
Dr. J. Kliewer
Homework 7
Due: March 30, 2015, beginning of class
Reading: Textbook sections 9.1, 9.2, 9.3
Problems from text
Department of Electrical and Computer Engineering, New Jersey Institute of Technology
ECE 673: Random Signal Analysis I
Homework Solutions (Week 1)
_
1.14
1.15
Page 1 of 4
1.16
Page 2 of 4
2.1
2.3
Page 3 of 4
2.10
2.14
Page 4 of 4
Department of Electrical and Computer Engineering, New Jersey Institute of Technology
ECE 673: Random Signal Analysis I
Homework Solutions (Week 4)
_
12.38
12.45
12.52
Page 1 of 5
12.56
Page 2 of 5
Page 3 of 5
13.4
13.8
Page 4 of 5
13.19
13.21
Page 5 of 5
Department of Electrical and Computer Engineering, New Jersey Institute of Technology
ECE 673: Random Signal Analysis I
Homework Solutions (Week 5)
_
14.1
14.10
14.13
Page 1 of 4
14.17
Page 2 of 4
15.2
Page 3 of 4
15.13
15.21
Page 4 of 4
Department of Electrical and Computer Engineering, New Jersey Institute of Technology
ECE 673: Random Signal Analysis I
Homework Solutions (Week 8)
_
Th
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ar stu
ed d
vi y re
aC s
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ou urc
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eH w
er as
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16.7
https:/www.coursehero.com/file/12
ECE673852 - Random Signal Analysis I
Week 4 examples
Example: A bank operates both a drive-up facility anda walk-up window. On a randomly
selected day, let X be the proportion of time that thedrive-up facility is in use, and Y is
the proportion of time th
Department of Electrical & Computer Engineering
New Jersey Institute of Technology
ECE 673: Random Signal Analysis
April 21, 2015
Dr. J. Kliewer
Homework 9: Solutions
Problem 9.54:
a)
E [X (t)]
CXX (t1 , t2 )
= E [A cos t + B sin t] = E [A] cos t + E [B]
Department of Electrical & Computer Engineering
New Jersey Institute of Technology
ECE 673: Random Signal Analysis
February 16, 2015
Dr. J. Kliewer
Homework 3: Solutions
Problem 3.28:
4
3
2
1
+1
+0
+ (1)
=1
10
10
10
10
3
1
20
4
+1
+1
=
=2
E[Y 2 ] = 4
10
Department of Electrical & Computer Engineering
New Jersey Institute of Technology
ECE 673: Random Signal Analysis
March 30, 2015
Dr. J. Kliewer
Homework 8: Solutions
Problem 9.21:
(a)
P [Yn = 1] = P [In is not erased |In = 1] P [In = 1]
= (1 ) p where In
Department of Electrical & Computer Engineering
New Jersey Institute of Technology
ECE 673: Random Signal Analysis
January 30, 2015
Dr. J. Kliewer
Homework 1: Solutions
Problem 2.14:
(a) (A B c C c ) (Ac B C c ) (Ac B c C)
(b) (A B C c ) (A B c C) (Ac B C
Department of Electrical & Computer Engineering
New Jersey Institute of Technology
ECE 673: Random Signal Analysis
February 23, 2015
Dr. J. Kliewer
Homework 4
Due: March 2, 2015, beginning of class
Reading: Textbook sections 5.2-5.7
Problems from textbook
Department of Electrical & Computer Engineering
New Jersey Institute of Technology
ECE 673: Random Signal Analysis
January 30, 2015
Dr. J. Kliewer
Homework 1
Due: February 6, 2015, beginning of class
Reading: Textbook sections 1, 2.1-2.2, 2.4-2.5, 3.1-3.2
Department of Electrical & Computer Engineering
New Jersey Institute of Technology
ECE 673: Random Signal Analysis
February 7, 2015
Dr. J. Kliewer
Homework 2
Due: February 17, 2015, beginning of class
Reading: Textbook sections 3.5, 4.3-4.5
Problems from
Department of Electrical & Computer Engineering
New Jersey Institute of Technology
ECE 673: Random Signal Analysis
February 23, 2015
Dr. J. Kliewer
Homework 5: Solutions
Problem 5.61:
(i)
1
1
1
+0 +1 =0
3
3
3
E [Y ] = 0 same pmf
1
1
E [XY ] = (1) (1) + (1
Department of Electrical & Computer Engineering
New Jersey Institute of Technology
ECE 673: Random Signal Analysis
February 23, 2015
Dr. J. Kliewer
Homework 4: Solutions
Problem 5.11:
(i)
X\Y
1
0
1
P [X = i] = 31
P [Y = i] = 31
P [X > 0] = 13
P [X > Y ] =
Department of Electrical & Computer Engineering
New Jersey Institute of Technology
ECE 673: Random Signal Analysis
March 23, 2015
Dr. J. Kliewer
Homework 7: Solutions
Problem 7.29:
The total number of errors S100 is the sum of iid Bernoulli random variabl
ECE673852 - Random Signal Analysis I
Week 5 examples
Example
A certain basketball player makes 80 percent of his free throws on average. What is the
probability that in 100 attempts he will be successful more than 85 times? Assume independence.
Solution I
Department of Electrical and Computer Engineering, New Jersey Institute of Technology
ECE 673: Random Signal Analysis I, Spring 2016
Homework Set 1 Solutions
_
Page 1 of 6
10.44 (f) If X : N (0,1) is transformed according to Y = exp(X), determine pY (y) b
INTUITIVE PROBABILITY
AND
RANDOM PROCESSES
USING MATLAB
INTUITIVE PROBABILITY
AND
RANDOM PROCESSES
USING MATLAB
STEVEN M. KAY
University of Rhode Island
^ Springer
Steven M. Kay
University of Rhode Island
Dept. of Electrical & Computer
Engineering
Kingsto
Department of Electrical and Computer Engineering, New Jersey Institute of Technology
ECE 673: Random Signal Analysis I, Spring 2016
Homework Set 5 Solutions
_
Page 1 of 6
Page 2 of 6
19.1 (w) Two discrete-time random processes are defined as X[n] = U[n]
Department of Electrical and Computer Engineering, New Jersey Institute of Technology
ECE 673: Random Signal Analysis I, Spring 2016
Homework Set 4 Solutions
_
17.39 (c) For the AR random processes whose ACSs are shown in Figure 17.6
generate a realizatio
Department of Electrical and Computer Engineering, New Jersey Institute of Technology
ECE 673: Random Signal Analysis I, Spring 2016
Homework Set 2 Solutions
_
12.45 (w, f) Two independent random variables X and Y have zero means and
variances of 1. If th