ECE 531: Detection and Estimation Theory, Spring 2011
Homework 11 Solutions
Problem1. (5.14 Shu Wang)
From Eq 5.5 and 5.6, we have:
T (x) = xT Cs (Cs + 2 I )1 x
s = Ah
2
Cs = E [ssT ] = E [AhAhT ] = E [AA]hhT = A hhT
2
2
T (x) = xT A hhT (A hhT + 2 I )1
ECE 531 Detection and Estimation - Final Exam
May 8, 2009. 8 am - 10 am in ERF 1003.
This exam has 6 questions. You will be given 2 hours. You may use the 2 course textbooks but no other aides/notes. No calculators are permitted. No talking, passing note
ECE 531: Detection and Estimation Theory, Spring 2011
Homework 1
ALL SOLUTIONS BY Shu Wang thanks for submitting latex le in 1st homework!
Problem1 (2.1)
Solution:
1
E [ 2 ] = E [
N
=
1
N
N 1
x2 [n]
n=0
N 1
E [x2 [n]
n=0
1
= N 2
N
= 2
So this is an unbias
University of Illinois at Chicago
Department of Electrical and Computer Engineering
EC 531: Detection and Estimation Theory
Spring 2009
Practice for Midterm 1
1. (30 points) You are a lawyer. In a community near Chicago, there is the suspicion that the gr
University of Illinois at Chicago
Department of Electrical and Computer Engineering
EC 531: Detection and Estimation Theory
Spring 2009
Midterm 2
NAME:
This exam has 4 questions.
You will be given the full class time: 75 minutes.
You may use the 2 cour
University of Illinois at Chicago
Department of Electrical and Computer Engineering
EC 531: Detection and Estimation Theory
Spring 2009
Midterm 2
NAME:
This exam has 4 questions.
You will be given the full class time: 75 minutes minutes.
You may use th
University of Illinois at Chicago
Department of Electrical and Computer Engineering
EC 531: Detection and Estimation Theory
Spring 2009
Midterm 1
NAME:
This exam has 4 questions.
You will be given the full class time: 75 minutes.
You may use the 2 cour
ECE 531: Detection and Estimation Theory, Spring 2011
Homework 10
Problem 1 (4.6 Luke Vercimak)
The this is a known signal in WGN. Per eq 4.3, the test statistic will be:
T (x) =
N 1
x[n]s[n] >
n=0
In this case (s[n] = Ar n ):
E=
For 0 < r < 1:
= A2
N 1
ECE 531: Detection and Estimation Theory, Spring 2011
Homework 8
Problem1. (13.4) (Shu Wang)
Solution:
From eq 13.5, we have:
n
2
2
Cs [m, n] = am+n+2 s + u amn
a2k
k=0
n
2
2
= amn (a2n+2 s + u
a2k )
k=0
From eq 13.6, we know that
n
2
2
var(s[n]) = Cs [n,
University of Illinois at Chicago
Department of Electrical and Computer Engineering
EC 531: Detection and Estimation Theory
Spring 2009
Final exam: PRACTICE
NAME:
This exam has 6 questions.
You will be given 2 hours.
You may use the 2 course textbooks
ECE 531: Detection and Estimation Theory, Spring 2011
Homework 6
Problem 1. (8.20) (Shu Wang)
Solution:
From the problem, we know that:
H =
1
r
.
.
.
r N 1
So we have h[n] = r n . According to 8.46, we have:
A(n) = A(n 1) + K [n](x[n] h[n]T A(n 1)
= A(n 1
ECE 531 - Detection and Estimation Theory
Homework 4
February 5, 2011
6.7 (Shu Wang) Assume that x[n] = As[n] + w[n] for n = 0, 1, . . . , N 1 are observed, where
w[n] is zero mean noise with covariance matrix C and s[n] is a known signal. The amplitude o
ECE 531 - Detection and Estimation Theory
Homework 2
Solutions
3.3 (Luke Vercimak) The data x[n] = Arn + w[n] for n = 0, 1, . . . , N 1 are observed, where
w[n] is WGN with variance 2 and r > 0 is known. Find the CRLB for A. Show that an
ecient estimator