Deemed University 2009 M.Tech Electronics and Communication Engineering University: Lingayas University Term: I Title of the : Signal Theory - Question Paper
Roll No. ..
Lingayas University, Faridabad
M.Tech (Electronics & Comm. Engg.) (Term I)
End Term Examination October, 2009
Course: Signal Theory
Course Code: EC -501
[Time: 3 Hours] [Max. Marks: 100]
Before answering the question, candidate should ensure that they have been supplied the correct and complete question paper. No complaint in this regard, will be entertained after examination.
Note: Question No. 1 Part A is compulsory. Attempt any two questions from Part B and any two questions from Part C. In all attempt five questions.
PART A
Q-1. (a) State Bayes Theorem of conditional probability. Illustrate it with an example (4)
(b) Give the concept of random variables. With an example explain the mapping of the sample space of an experiments a number line. (4)
(c) Explain the properties of a probability density function. (4)
(d) Write the relationship between cross-power spectrum and cross-correlation function. (4)
(e) Explain the Cramers-Rao inequity for non-random parameters (4)
PART B
Q-2. A joint probability density function is
fXY (x,y) = 
{ 
0 < x
< a and 0 <y < b
0 elsewhere
(a) Determine FXY (x,y) (10)
(b) If a < b find
(i) P 
(5)
(ii) P 
(5)
Q-3. (a) Derive expressions for available power gain, effective input noise temperature and spot noise figures. (10)
(b) Explain the functions of multiple random variables. (10)
Q-4. Random variables x and y have respective density functions.
Fx (x) = 
[ u (x) u
(x-a)]
Fy (y) = b u (y) e-by
Where a > 0 and b > 0, Determine the density function of W = X + Y if X and Y are statistically independent (20)
PART C
Q-5. (a) A random process is defined X(t) = A cos (pt)
Where A is a Gaussian
random variable with Zero mean and variance sA2. Determine the
density functions X (0) and X (1). Is X (t) stationary in any sense? (10)
(b) A random process consists of three sample functions X (t, s1) = 2
X (t, s2) = 2cos (t) and x (t, s3) = 3 sin (t) each occurring with equal probability. Is this process stationary in any sense. (10)
Q-6. Given two random processes X(t) and Y (t). Find expressions for auto correlation function of
W (t) = X (t) + Y (t) if
(a) X (t) and Y (t) are correlated (6)
(b) X (t) and Y (t) are uncorrelated (7)
(c) X (t) and Y (t) are uncorrelated with Zero means. (7)
Q-7. Show that if we use as estimate of the power spectrum S (w) of a discrete-time process x(n) the function
Sw (w) = 
Wm
R (m) e jwmt 14+6
= 20
Then
Sw (w) = 
S (y) w (w-y)
dy
And
W (w) = 
wn
e-jnwT
Find W (w) if N = 10 and
wn = 1 - 
Q-8. Write technical notes on any two of the following:
(a) Narrow band noise and properties
(b) Modeling of noise source
(c) Bayes estimation (20)
| Earning: Approval pending. |
