E13530 Homework # 6 . . . , -. .
Consider a random telegraph signai with RmCz) -= 201! , where o. is the average
transition rate of the signal
Co) Find the pits-wet" spectral density of the telegraph signal
Cb) This signal is passed through an
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M191 1 MM cfw_1
d! :3) -1 -2 :30) 1
mt! tho the solution 2(1) for the 9116:!me
21(0) a 1:116 23(0) :- 2
1J0 Deannim the manoabity Ind obscmbity of the dynmic system model given bciow
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This chapter is an introduction to WDM device issues. The reader needs
no background in optics or advanced physics. For a more advanced and/or
detailed discussion of WDM devices, we suggest t
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TABLE OF CONTENTS
EGEE 580 Equation Sheet Midterm #2
Probability Distribution Function
FX(X)=P(XSX) ; ny(x,y)=P(sz n YSy)
Probability Density Function
dx) d2 F(x,y)
f = f _ ._.
(x) dx (Ky) dxdy
YZ X2 A. ,
P 45x, 5 X 5 x2 d, 5 Y
1) Consider a normal WSS process X(t) with cfw_() = 0 and
() = 4 | . Find:
a) cfw_() 3
b) cfw_[( + 1) ( 1)]2
2) Consider a normal WSS process X(t) with cfw_() = 0 and () =
4 2| . We form the random variables Z = X(t+1) and W=X(t-1).
1) A call occurs at time t where t is a random point in the interval (0,10).
a) If A = cfw_2 5 and B = cfw_3 6, find A+B, AB, (A+B)AB
b) Find P(A), P(A| > 5)
2) A box 1 contains 1000 bulbs of which 10 percent are defective. Box 2
1) Let () = cos 2 , where is a random variable with mean and
a) Is () ergodic in the mean?
b) Is () ergodic in the autocorrelation function?
2) A W.S.S random process () has:
| > 1
() = cfw_
Is () mean ergodi
1) Two random variables X and Y have means = 1 and = 2, variances
2 = 4 and 2 = 1, and a correlation = 0.4. New random W and V are
defined by V = -X + 2Y and W = X + 3Y. Find:
a) The means
b) The variances
c) The correlation
d) The cor
1) Consider random variable X with the following density function:
() = (16 4 )
a) Determine the distribution function of X
b) Determine the f (x|) where B = cfw_1 1
c) Determine P (-1 2 | 1)
d) Determine the mean and the variance
545/0 #N #0293
/.4 What is the fundamental solution matrix of Exercise 2.2 when n = 1'? When n = 2?
SOLUTION TO EXERCISE 2.4 The fundamental solution matrix of a rst-order linear homogeneous
system of n differential equations '
.on an int
3C5 Tutorial Sheet 6
Dr. David Corrigan
18 March 2011
When examining analogue modulation schemes, it is often convenient to consider an
information signal with a single tone or frequency component (ie. a sinusoidal signal). Doing
so makes power and spectr
3.60. (a) The system is not LTI. (1/2)" is an eigen function of LTI systems. Therefore, the
output should have been of the form K (1 /2)", where K is a complex constant.
(b) It is possible to ﬁnd an LTI system with this input-output relationship.
ECE 316, Fall 2005
Solutions to Problem Set 7 - for tutorials week of November 7
Lathi, Chapter 5, nos 1.3, 2.1, 2.2, 2.7, 3,2
Solution Lathi 5.1.3
(a) P M (t) = A cos(c t + kp m(t) = 10 cos(10, 000t + kp m(t). Thus kp m(t) = 3000t. If
kp = 1000, m(t)3t.
HW: Angle Modulation
1. The angle modulated signal
(t) = 10 cos (2 108t + 200 cos 2 103t).
(a) Average power.
(b) Instantaneous frequency in Hz, and modulation index.
2. Consider the angle modulated signal
(t) = 10 cos (2 108t + 3 sin 2 103t).
First of all all employees must to be honest all times and all employees must have ethic
at the job. Driven by this statements the best option for us is that Bryan reports to Max's
supervisor. Is well known that the subordinate always have to obey your su
A Solution Manual and Notes for:
Kalman Filtering: Theory and Practice using MATLAB
by Mohinder S. Grewal and Angus P. Andrews.
John L. Weatherwax
April 30, 2012
Here youll nd some notes that I wrote up as I worked through this excellent book
OLUTION TO PROBLEM 3.7 Because the X; are independent with zero mean, the variance
End-41’») = Xi) (2X1) >
(n— 1) a}.
and the covariance
Consequently, the correlation coefﬁcient
KN; #wﬁs . r; of»
In this case the oontroﬂability matrix C has full rank, which can be demonstrated by computing the determinant of
its 2 x 2 symmetric product
implying that this system model is controllable.
2.11 Derive the s
A Kalman filter control technique in meanvariance portfolio management
Journal of Economics and Finance
J Econ Finan
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rights are held exclusivel
12 LINEAR DYNAMIC SYSTEMS
— ~1+’ 1+‘ _ 3"
2: E 2 —%+—:——%
This solution also satisﬁes the initial conditions
£13310) = 93(0).
Problem 2.7 Find the total solution and state transition matrix for the system
Problem 3.27 Let S(t) and n(t) be real stationary uncorrelated RPs, each with mean zero.
Here, H 1 (ﬁnal), H 2 (j21rw), and H3 (j21rw) are transfer functions of time-invariant linear systems and So (t)
is the output when n(t) is zero and no (t) is th
Prove the condition in the discussion following Equation 4.9 that EWkZT for i = 1, . k when Wk and Vk are uncorrelated and white.
In Example 4:4, use white noise as a driving input to range rate (i'k) and bearing rate (8k) equations instead of