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 best alternative in the following: (2x10)
a. Two sequences 
and 
are related by 
. In the
Z-domain, their ROC are
(A) same (B) reciprocal of each other
(C) negative of each other (D) complement of each other
b. The autocorrelation of a sinusoid is
(A) Sinc pulse (B) another sinusoid
(C) Rectangular pulse (D) Triangular pulse
c. Which of the
following is true for the system represented by 
(A) Linear (B) Time invariant
(C) Causal (D) Non Linear
d. The fourier transform of impulse function is
(A)
(B)
(C) 1 (D)
e. Convolution is used to find
(A) amount of similarity between the signals
(B) response of the system
(C) multiplication of the signals
(D) Fourier transform
f. The final value
of 
is
(A) 2 (B) 3
(C) 
(D) 0
g. Discrete time system is stable if the poles are
(A) within unit circle (B) outside unit circle
(C) on the unit circle (D) None
h. The z
transform of 
is
(A)
(B)
(C) 
(D)
i. The area under
Gaussian pulse 
is
(A) Unity (B) Infinity
(C) Pulse (D) Zero
j. The spectral density of white noise is
(A) Exponential (B) Uniform
(C) Poisson (D) Gaussian
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. Check whether the following signals are energy or power signal and hence find the corresponding energy or power? (6)
(i)
(ii)
b. Find the convolution of two rectangular pulse signals shown below (10)
 |
Q.3 a. Given
the Gaussian pulse 
determine its fourier transform. (8)
b. Find the exponential Fourier Series of the following signal? (8)
|
Q.4 a. State and prove the following properties of DTFT. (6)
(i) Time shifting, frequency shifting
(ii) Conjugate symmetry
(iii) Time reversal.
b. Consider a stable Causal
LTI system whose input 
and output 
are related through
second order difference equation
determine the response for the
given input 
(10)
Q.5 a. A continuous time signal is given below
(8)
Determine
(i) Minimum sampling rate
(ii) If fs=400Hz what is discrete time signal obtained after sampling.
(iii) If fs=150Hz what is discrete time signal obtained after sampling.
b. State and prove Parsevals theorem for Continuous domain periodic signal. (8)
Q.6 a. Compute the Magnitude and Phase of the Frequency Response of the First order Discrete time LTI system given by equation (10)
b. Determine the Fourier
Transform of unit step
(6)
Q.7 a. By using convolution theorem determine the inverse Laplace transform of the following functions (8)
(i)
(ii) 
b. Check the stability & causality of a continuous LTI system described as
(8)
Q.8 a. Find
the 
-Transform 
and sketch the pole-zero with the
ROC for each of the following sequences. (8)
(i)
(ii)
b. Determine
the inverse Transform of 
if the region of convergence
are (i) 
(ii)
(iii)
(8)
Q.9 a. Consider
the probability density function 
where X is a random variable whose
allowable value range from 
to 
. Find
(i) Commulative distribution
function 
(ii) Relationship between a and b.
(iii)
(8)
Determine mean, mean square and Variance.
b. Find the power spectral
density for the cosine signal 
and also compute power in the signal. (8)