Gujarat Technological University 2010 M.E Statistical Signal Analysis - Question Paper
Saturday, 20 July 2013 08:50Web
Page 1 of 2
GUJARAT TECH OLOGICAL U IVERSITY
M.E Sem-I exam January 2010
Subject code: 710401 Subject ame: Statistical Signal Analysis
Total Marks: 60
Instructions:
1. Attempt all ques..
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) provide ans of subsequent ques.. 06
1.
2.
3.
define the use of probability theory in Communication Engineering.
discuss the meaning of statistical independent ness and uncorrelated ness of two
random variables. Out of these 2 parameters of random variable which is the
stronger notion of independent ness.
A uniformly distributed Random variable X has Probability Density Function (PDF)
fX(x) =1/2p, 0= X = two p .
obtain the expected value of cos(x) (i.e. E [cos(x)]) and expected value of x2 (i.e.
E[x2].)
(b) provide ans of subsequent ques.. 06
1.
2.
Someone has provided you the Cumulative Distribution Function(CDF) of random
variable as,
/ one x 0
( )
0 x<0
x b
X
ae
F x
? - - =
=?
?
As you are expert in Statistical Signal Analysis (SSA) she asks you to verify
whether FX(x) is a valid CDF or not. provide your ans to her query.
The Probability Density Function (PDF) of exponential distributed random X is
provided as ( ) 0 0 x
X f x e x and = ? -? = ? > . obtain the characteristics function of
random variable X.
Q.2 (a)
In mobile radio communication when any obstruction (e.g. like hill or tall building)
comes in to the path of signal then the region behind obstruction is called shadow
region and only diffracted signal will reach to mobile unit, as shown in figure below,
If transmitted signal has Gaussian distribution with mean mx and variance s2 than
obtain distribution of received signal in scattering zone. See the figure beneath.
06
[Hint: In scattering zone received signal random variable is Y, then Y=eX . where X
is the transmitted signal random variable]
(b)
1.
2.
provide ans of subsequent ques..
Let Z be the random variable with PDF ( ) Z f z =1/2. Let new random variable X and
Y is described as, X=Z and Y=Z2. X and Y both are uncorrelated? X and Y both are
statistically independent?
The PDF of continuous random variable X is provided as
3.1437 1
0 otherwise
x
X
e
f x
? -
=?
?
obtain the probability that X takes a value greater than two provided that it has a value
greater then 1.5.
06
OR
(b)
1.
2.
provide ans of subsequent ques..
provide the PDF for Gaussian distributed random variable and show that Gaussian PDF
integrates to one.
A communication system accepts a positive voltage V as a input and outputs a
voltage Y=aV+N , where a=10-2 and N is a Gaussian random variable with
| Earning: Approval pending. |
