AMIETE – ET/CS/IT (OLD SCHEME)
Code:
AE06/ AC04/ AT04 Subject:
SIGNALS & SYSTEMS
Time: 3 Hours Max. Marks: 100
NOTE: There are 9 Questions in all.
· Question 1 is compulsory and carries 20 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.
· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.
· Any required data not explicitly given, may be suitably assumed and stated.
Q.1 Choose
the correct or the best alternative in the following: (2
10)
a. The Fourier transform of 
(A) 
(B)
(C)
(D)
b. Consider a continuous-time system with input x(t) and output y(t)
related by 
.
The system is
(A) Linear (B) Causal
(C) Non-linear (D) Non-causal
c. The equation 
is also called
as
(A) Superposition integral (B) Continuous integral
(C) Time integral (D) None of the above
d. According to time
shifting property of Fourier transform, 
is equal to
(A)
(B)
(C) 
(D)
e. Parseval’s
relation for a periodic signals 
equal to
(A)
(B)
(C) 
(D)
None of the above
f. The discrete
fourier transform of 
is equal to
(A)
(B)
(C) 
(D)
g. An ideal low pass filter is
(A) Causal (B) Non-causal
(C) Inverse causal (D) None
h. If 
with ROC=R, then
Laplace transform of 
is equal to
(A)
(B)
(C) 
(D)
i. For a causal linear time invariant system, the impulse response for t < 0 is equal to
(A) Unity (B) Infinity
(C) Zero (D) None
j. The ROC associated with the system function for a causal system is a
(A) Right half plane (B) Left half plane
(C) Middle of plane (D) None of the above
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. Find
out whether signal 
is an energy signal or a power signal.
Also find if 
is
an energy signal or a power signal. (8)
b. Find
out the response of a continuous –time system to unit step input given the
impulse response, 
. (8)
Q.3 a. Find the trigonometric Fourier series for the waveform shown in Fig.1. (8)
|
b. Determine
the fourier series coefficients 
for a discrete-time periodic signal
given as 
,
where 
.
(8)
Q.4 a. Determine the continuous-time
fourier transform of a continuous –time signal, 
. (8)
b. Find the fourier transform of the pulse shown in Fig.2 below (8)
|
Q.5 a. Using discrete
time fourier transform, determine the frequency response and impulse response
of a causal discrete-time LTI system that is characterised by, 
. (8)
b. Determine
the discrete-time frequency transform of the discrete-time periodic signal, , with fundamental
frequency 
. (8)
Q.6 a. The frequency response for a causal and stable
continuous time LTI system is given by, 
.
(i) Find the magnitude of 
.
(ii) Determine which
of the following statement is true about 
, the group delay of the system
1.
2.
3.
(8)
b. Find the Nyquist rate
and Nyquist interval for the continuous-time signal, 
. (8)
Q.7 a. Find
the z-transform and ROC for the signal sequence 
. (6)
b. State initial value theorem for z-domain transfer function. Find the initial
value
of the corresponding sequence, s(n) having a z-transform 
. (6)
c. Determine the
sequence s(n) whose z-transform 
. (4)
Q.8 a. A binary source generates digits 1 and 0 randomly with probabilities 0.6 and 0.4 respectively.
(i) What is the probability that two 1’s and three 0’s will occur in a five-digit sequence?
(ii) What is the probability that atleast three 1’s will occur in a five-digit sequence? (6)
b. The
pdf of a random variable X is given by, 
where, K is a constant
(i) Determine the value of K.
(ii)
Let a = -1 and b=2. Calculate 
. (6)
c. Consider a random process X(t)
given by, 
;
where 
is
a random variable uniformly distributed in the range 
. Show that the process is
ergodic in the mean. (4)
Q.9 Write short notes on:
(i) Joint probability.
(ii) Conditional probability.
(iii) Cross spectral density.
(iv)
White
noise. (44 = 16)