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GATE SOLVED PAPERElectronics & Communication Signals &
Systems
Copyright By NODIA & COMPANY
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2013 ONE MARK
Q. 1 Two systems with impulse responses h t1^ h and h t2^ h are
connected in cascade. Then the overall impulse response of the
cascaded system is given by(A) product of h t1^ h and h t2^ h
(B) sum of h t1^ h and h t2^ h
(C) convolution of h t1^ h and h t2^ h
(D) subtraction of h t2^ h from h t1^ h
Q. 2 The impulse response of a system is h t tu t=^ ^h h. For an
input u t 1-^ h, the output is
(A) t u t22
^ h (B) t t
u t21
1-
-^ ^h
h
(C) t
u t21
12-
-^ ^h
h (D) t u t21 1
2- -^ h
Q. 3 For a periodic signal /sin cos sinv t t t t30 100 10 300 6
500 4p= + + +^ ^h h, the fundamental frequency in /rad s(A) 100 (B)
300
(C) 500 (D) 1500
Q. 4 A band-limited signal with a maximum frequency of 5 kHz is
to be sampled. According to the sampling theorem, the sampling
frequency which is not valid is(A) 5 kHz (B) 12 kHz
(C) 15 kHz (D) 20 kHz
Q. 5 Which one of the following statements is NOT TRUE for a
continuous time causal and stable LTI system?(A) All the poles of
the system must lie on the left side of the jw axis(B) Zeros of the
system can lie anywhere in the s-plane
(C) All the poles must lie within s 1=(D) All the roots of the
characteristic equation must be located on the left side
of the jw axis.
Q. 6 Assuming zero initial condition, the response y t^ h of the
system given below to a unit step input u t^ h is
(A) u t^ h (B) tu t^ h
(C) t u t22
^ h (D) e u tt- ^ h
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GATE SOLVED PAPER - EC SIGNALS & SYSTEMS
Q. 7 Let g t e t2
= p-^ h , and h t^ h is a filter matched to g t^ h. If g t^ h is
applied as input to h t^ h, then the Fourier transform of the
output is(A) e f
2p- (B) e /f 22p-
(C) e fp- (D) e f22p-
2013 TWO MARKS
Q. 8 The impulse response of a continuous time system is given
by h t t t1 3d d= - + -^ ^ ^h h h. The value of the step response
at t 2= is(A) 0 (B) 1
(C) 2 (D) 3
Q. 9 A system described by the differential equation dtd y
dtdy y t x t5 62
2
+ + =^ ^h h. Let x t^ h be a rectangular pulse given by
x tt
otherwise10
0 2< , when the forcing function is x t^ h and the initial
condition is y 0^ h. If one wishes to modify the system so that the
solution becomes y t2- ^ h for t 0> , we need to(A) change the
initial condition to y 0- ^ h and the forcing function to x t2 ^
h(B) change the initial condition to y2 0^ h and the forcing
function to x t- ^ h(C) change the initial condition to j y2 0^ h
and the forcing function to
j x t2 ^ h
(D) change the initial condition to y2 0- ^ h and the forcing
function to x t2- ^ h
Q. 11 The DFT of a vector a b c d8 B is the vector a b g d8 B.
Consider the product
p q r s8 B a b c d
adcb
badc
cbad
dcba
=
R
T
SSSSSS
8
V
X
WWWWWW
B
The DFT of the vector p q r s8 B is a scaled version of(A) 2 2 2
2a b g d9 C (B) a b g d9 C(C) a b b d d g g a+ + + +8 B (D) a b g
d8 B
2012 ONE MARK
Q. 12 The unilateral Laplace transform of ( )f t is s s 1
12+ +
. The unilateral Laplace transform of ( )tf t is
(A) ( )s s
s12 2
-+ +
(B) ( )s s
s1
2 12 2- + +
+
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(C) ( )s s
s12 2+ +
(D) ( )s s
s1
2 12 2+ +
+
Q. 13 If [ ] (1/3) (1/2) [ ],x n u nn n= - then the region of
convergence (ROC) of its z-transform in the z -plane will be
(A) z31 3< < (B) z3
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