2014 EE01 ONE MARK
EE SP 2.1 Let X s
s2 310s s5 21 =
+ ++
^ h be the Laplace Transform of a signal x t^ h. Then, x 0^ h+
is
(A) 0 (B) 3
(C) 5 (D) 21
EE SP 2.2 For a periodic square wave, which one of the following statements is TRUE ? (A) The Fourier series coefficients do not exist.
(B) The Fourier series coefficients exist but the reconstruction converges at no point.
(C) The Fourier series coefficients exist and the reconstruction converges at most points.
(D) The Fourier series coefficients exist and the reconstruction converges at every point.
2014 EE02 TWO MARKS
EE SP 2.3 Let f t^ h be a continuous time signal and let F w ^ h be its Fourier Transform defined by F w ^ h = f t e j tdt 3 3 -w - ^ h
#
Define g t^ h by g t^ h = F u e jutdu 3 3 - - ^ h#
What is the relationship between f t^ h and g t^ h ? (A) g t^ h would always be proportional to f t^ h
(B) g t^ h would be proportional to f t^ h if f t^ h is an even function
(C) g t^ h would be proportional to f t^ h only if f t^ h is a sinusoidal function (D) g t^ h would never be proportional to f t^ h
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(A) u t^ h-u t^ -Th+^t-TThu t^ -Th-^t-T2Thu t^ -2Th (B) u t^ h+Tt u t T^ - h-Tt u t^ -2Th (C) u t^ h-u t^ -Th+^t-TThu t^ h-^t-T2Thu t^ h (D) u t^ h+^t-TThu t^ -Th-2^t-T2Thu t^ -2Th2014 EE02 ONE MARK
EE SP 2.5 Consider an LTI system with transfer function
H s^ h
s s1 4 =
+
^ h
If the input to the system is cos t^ h3 and the steady state output is Asin^3t+a h
, then the value of A is
(A) 1/30 (B) 1/15
(C) 3/4 (D) 4/3
EE SP 2.6 Consider an LTI system with impulse response h t^ h=e u t-5t ^ h. If the output of
the system is y t^ h=e u t-3t ^ h-e u t-5t ^ h then the input, x t^ h, is given by
(A) e u t-3t ^ h
(B) 2e u t-3t ^ h
(C) e u t-5t ^ h
(D) 2e u t-5t ^ h
2014 EE02 TWO MARKS
EE SP 2.7 A discrete system is represented by the difference equation
X k X k 1 1 1 2 + + ^ ^ hh > H aa 1 aa 1 X kX k1 2 => + - H> ^^ hhH
It has initial conditions X1^0h=1;X2^0h=0. The pole locations of the system
for a=1, are (A) 1!j0
(B) -1!j0
(C) !1+j0
(D) 0!j1
EE SP 2.8 An input signal x t^ h= +2 5sin^100p th is sampled with a sampling frequency of
Hz
400 and applied to the system whose transfer function is represented by
X z Y z ^ ^ h h N1 11 zz N 1 = - - - - c m
where, N represents the number of samples per cycle. The output y n^ h of the system under steady state is
(A) 0 (B) 1
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2014 EE03 ONE MARK
EE SP 2.9 A function f t^ h is shown in the figure.
The Fourier transform F w ^ h of f t^ h is (A) real and even function of w
(B) real and odd function of w
(C) imaginary and odd function of w
(D) imaginary and even function of w
EE SP 2.10 A signal is represented by x t^ h t t 1 1 0 1 < > =
*
The Fourier transform of the convolved signal y t^ h=x t^2 h*x t^/2h is (A) 42sin 2 sin 2
w awk ^ wh (B) w42sina kw2
(C) 42sin 2
w ^ hw (D) w42sin2w
EE SP 2.11 For the signal f t^ h=3sin8pt+6sin12pt+sin14pt, the minimum sampling frequency (in Hz) satisfying the Nyquist criterion is _____.
2014 EE03 TWO MARKS
EE SP 2.12 A continuous-time LTI system with system function H w ^ h has the following pole- zero plot. For this system, which of the alternatives is TRUE ?
(A) H 0 > w ^ h ^ h ; w >0
(B) H w ^ h has multiple maxima, at w 1 and w 2
(C) H^0 <h H^w h ; w >0
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EE SP 2.13 A sinusoid x t^ h of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with cutoff at 25Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that x t^ h
(A) 10 Hz (B) 60 Hz
(C) 30 Hz (D) 90 Hz
EE SP 2.14 A differentiable non constant even function x t^ h has a derivative y t^ h, and their respective Fourier Transforms are X w ^ h and Y w ^ h. Which of the following statments is TRUE ?
(A) X w ^ h and Y w ^ h are both real (B) X w ^ h is real and Y w ^ h is imaginary (C) X w ^ h and Y w ^ h are both imaginary (D) X w ^ h is imaginary and Y w ^ h is real
YEAR 2013 ONE MARK
EE SP 2.15 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
EE SP 2.16 For a periodic signal v t^ h=30sin100t+10cos300t+6sin^500t+p/4h, the fundamental frequency in rad s/
(A) 100 (B) 300
(C) 500 (D) 1500
EE SP 2.17 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
EE SP 2.18 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.
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output is (A) t u t22 ^ h (B) t t^ -2 1hu t^ -1h (C) t 21 u t 1 2 - - ^ h ^ h (D) t2-2 1u t^ -1hYEAR 2013 TWO MARKS
EE SP 2.20 The impulse response of a continuous time system is given by h t^ h=d^t-1h+d^t-3h
. The value of the step response at t=2 is
(A) 0 (B) 1
(C) 2 (D) 3
YEAR 2012 ONE MARK
EE SP 2.21 If x n[ ]=(1/3)n -(1/2)nu n[ ], then the region of convergence (ROC) of its z
-transform in the z-plane will be
(A) 31 < z <3 (B) 13< z <21
(C) 12< z <3 (D) 31 < z
EE SP 2.22 The unilateral Laplace transform of f t( ) is
s s 1
1
2+ + . The unilateral Laplace
transform of tf t( ) is (A) (s2 ss 1)2 - + + (B) -(s22+ +ss+11)2 (C) (s s ) s 1 2+ + 2 (D) (s22+ +ss+11)2
YEAR 2012 TWO MARKS
EE SP 2.23 Let y n[ ] denote the convolution of h n[ ] and g n[ ], where h n[ ]=( / )1 2 nu n[ ] and [ ]
g n is a causal sequence. If y[0]=1 and y[1]=1/2, then g[1] equals (A) 0
(B) 1 2/
(C) 1 (D) 3 2/
EE SP 2.24 The Fourier transform of a signal h t( ) is H j( )w =(2cosw)(sin2w w)/ . The value of h 0( ) is
(A) 1 4/
(B) 1 2/
(C) 1 (D) 2
EE SP 2.25 The input x t( ) and output y t( ) of a system are related as y t( )= tx( )t cos(3 )t td 3
-
#
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(A) time-invariant and stable (B) stable and not time-invariant (C) time-invariant and not stable (D) not time-invariant and not stable
YEAR 2011 ONE MARK
EE SP 2.26 The Fourier series expansion f t( ) a ancosn t b sinn t
n n 0 1 w w = + 3 + =
/
ofthe periodic signal shown below will contain the following nonzero terms
(A) a0 and b nn, =1 3 5, , ,...3
(B) a0 and a nn, =1 2 3, , ,...3
(C) a a0 n and b nn, =1 2 3, , ,...3
(D) a0 and a nn =1 3 5, , ,...3
EE SP 2.27 Given two continuous time signals x t( )=e-t and y t( )=e-2t which exist for
t>0, the convolution z t( )=x t y t( ) ( )* is
(A) e-t-e-2t
(B) e-3t
(C) e+t
(D) e-t+e-2t
YEAR 2011 TWO MARKS
EE SP 2.28 Let the Laplace transform of a function f t( ) which exists for t>0 be F s1( )
and the Laplace transform of its delayed version f t( -t) be F s2( ). Let F1* ( )s
be the complex conjugate of F s1( ) with the Laplace variable set s = +s jw. If ( ) ( ) ( ) * ( ) G s F s F s F s 1 2 2 1
= , then the inverse Laplace transform of G s( ) is an ideal (A) impulse d( )t
(B) delayed impulse d(t-t)
(C) step function u t( )
(D) delayed step function u t( -t)
EE SP 2.29 The response h t( ) of a linear time invariant system to an impulse d( )t , under initially relaxed condition is h t( )=e-t+e-2t. The response of this system for a
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unit step input u t( ) is (A) u t( )+e-t+e-2t
(B) (e-t+e-2t) ( )u t
(C) ( .1 5-e-t-0 5. e-2t) ( )u t
(D) e-td( )t +e u t-2t ( )
YEAR 2010 ONE MARK
EE SP 2.30 For the system /(2 s+ , the approximate time taken for a step response to 1) reach 98% of the final value is
(A) 1 s (B) 2 s (C) 4 s (D) 8 s
EE SP 2.31 The period of the signal ( )x t 8sin 0.8 t
4 p p = ` + j is (A) 0.4p s (B) 0.8p s (C) 1.25 s (D) 2.5 s
EE SP 2.32 The system represented by the input-output relationship ( )y t = 5tx( )t td t, >0
3 -
#
is(A) Linear and causal (B) Linear but not causal (C) Causal but not linear (D) Neither liner nor causal
EE SP 2.33 The second harmonic component of the periodic waveform given in the figure has an amplitude of
(A) 0 (B) 1 (C) /2 p (D) 5
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YEAR 2010 TWO MARKS
EE SP 2.34 x t is a positive rectangular pulse from ( ) t=-1tot=+ with unit height as 1 shown in the figure. The value of X( )w 2dw whereX( )w
3 3 - "
#
is the Fourier transform of ( )}x t is. (A) 2 (B) 2p (C) 4 (D) 4pEE SP 2.35 Given the finite length input [ ]x n and the corresponding finite length output [ ]y n
of an LTI system as shown below, the impulse response [ ]h n of the system is
(A) - [ ] {1, 0, 0, 1} h n = (B) - [ ] {1, 0, 1} h n = (C) - [ ] {1, 1, 1, 1} h n = (D) - [ ] {1, 1, 1} h n =