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IES E & T Topic wise QuestionsSignal & Systems
www.gatehelp.com
YEAR 1999
MCQ 1
Assertion (A) : An LTI discrete system represented by the difference equation ( ) ( ) ( ) ( )y n y n y n x n2 5 1 6+ + + = in unstable.
Reason (R) : A system is unstable if the roots of the characteristic equation lie outside the unit circle.
(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true but R is NOT the correct explanation of A.
(C) A is true but R is false.
(D) A is false but R is true.
MCQ 2
Match List I (Characteristic of ( )f t ) with List II (Functions) ans select the correct answer using the codes given below the lists :
List I List II
A. ( )( ( ))f t u t1 0 = 1. Decaying exponential
B. ( ) ( )/ ;f t Kdf t dt 0+ =K is a positiveconstant
2. Growth exponential
C.( )
( )f t K
dtd f t
022
+ = ;
K is a positive constant
3. Impulse
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D. ( )( ( ) ( ))f t g t g 0 0 = ;for any arbitrary ( )g t
4. Causal
5. Sinusoid
Codes :
A B C D
(A) 4 1 5 3
(B) 1 4 5 3
(C) 4 2 5 1
(D) 2 5 4 1
MCQ 3
Which one of the following pairs is NOT correctly matched ?
(Input ( )x t and output ( )y t )
(A) Unstable system : ( )
. ( ) ( )dtdy t
y t x t0 1 =
(B) Nonlinear system : ( )
( ) ( )dtdy t
t y t x t2 2+ =
(C) Noncausal system : ( ) ( )y t x t 2= +
(D) Nondynamic system : ( ) ( )y t x t3 2=
MCQ 4
If a plot of signal ( )x t is as shown in the Fig.-1
Then the plot of the signal ( )x t1 will be
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IES E & T Topicwise 1999-2009Signal & Systems
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MCQ 5
The state model
( )x k 1+ ( ) ( )x k u k0 1 0
1 = +> >H H ( )y k
( )( )
x kx k0 1
1
2= 8 >B H
is represented in the difference equation as(A) ( ) ( ) ( ) ( )c k c k c k u k2 1 + + + + =
(B) ( ) ( ) ( ) ( )c k c k c k u k1 1 1 + + + =
(C) ( ) ( ) ( ) ( )c k c k c k u k2 1 + + =
(D) ( 1) ( ) ( 1) ( 1)c k c k c k u k + + + = +
MCQ 6
The signal (1 4 ) ( )cos cosM t t2 103# + contains the frequency component (in Hz)
(A) 998,1000 and 1002
(B) 1000 and 2000
(C) dc 2 and 1000
(D) ........,996, 998, 1000, 1002, 1004, .......
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MCQ 7
Which one of the following input-output relationship is that of a linear system ?
MCQ 8
The discrete-time equation ( ) . ( ) . ( )y n ny n x n1 0 5 0 5 1+ + = + is NOT attributable to a
(A) memoryless system
(B) time-varying system
(C) linear system
(D) causal system
MCQ 9(A) 1/8 s
(B) 8 s
(C) 4 s
(D) 1/4 s
MCQ 10
Match List I (Fourier transform) with List II (Functions of time) and select the correct answer using the codes given below the lists :
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List I List II
A. sink 1. A constant
B. e j d 2. Exponential function
C.( )j 2
12+
3. t -multiplied exponential function
D. ( )k 4. Rectangular pulse
5. Impulse function
Codes :
A B C D
(A) 4 5 3 1
(B) 4 5 3 2
(C) 3 4 2 1
(D) 3 4 2 5
MCQ 11
Laplace transform of ( )sin t + is
(A) ( / )exp ss2 2 +
(B) ( / )exp ss2 2 +
(C) ( / )exp sss
2 2
+
(D) ( / )exp ss2 2 +
MCQ 12
The function ( )f t shown in the given figure will have Laplace transform as
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(A) s s
ese1 1 1s s2 2
2
(B) ( )s
e e1 1 s s22
(C) ( )s e e1 1 s s2
(D) ( )s e se1 1 s s2
MCQ 13
Inverse Laplace transform of the function s s
s5 6
2 52+ ++ is
(A) ( . ) .exp cosht t2 2 5 0 5
(B) ( ) ( )exp expt t2 3
(C) ( . ) .exp sinht t2 2 5 0 5
(D) ( . ) .exp cost t2 2 5 0 5
MCQ 14
Fig. I and Fig.II show respectively the input ( )x t to a linear time-invarient system and the impulse response ( )h t of the system.
The output of the system is zero everywhere except for the time-interval
(A) t0 4< 3. f t0 a k
D. ( / )exp j t t2 0 4.f2
22 2
+ ^ hCodes :
A B C D
(A) 3 1 4 2
(B) 2 4 1 3
(C) 3 4 1 2
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(D) 2 1 4 3
MCQ 53
Match List I (Type of signal) with List II (property of Fourier transform) and select the correct answer using the codes given below the lists :
List I List II
A. Real and even symmetric 1. Imaginary and even symmetric
B. Real and odd symmetric 2. Real and even symmetric
C. Imaginary and even symmetric 3. Real odd symmetric
D. Imaginary and odd symmetric 4. Imaginary and odd symmetric
Codes :
A B C D
(A) 1 4 2 3
(B) 2 4 1 3
(C) 1 3 2 4
(D) 2 3 1 4
MCQ 54
Consider the following statements :
1. Fourier transform is special case of Laplace transform
2. Region of convergence need not be specified for Fourier transform
3. Laplace transform is not unique unless the region of convergence is specified
4. Laplace transform is a special case of Fourier transform
Which of these statements are correct ?
(A) 2 and 4
(B) 4 and 1
(C) 4, 3 and 2
(D) 1, 2 and 3
MCQ 55
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The response of a linear, time-invariant discrete-time system to a unit step input ( )u n is the unit impulse ( )n . The system response to a ramp input n ( )u n would be
(A) ( )u n
(B) ( )u n 1
(C) ( )n n
(D) ( )k n Kk 0
3
=/
MCQ 56
If ( )X zz zz z
1
3
=++
then ( )x n series has
(A) alternate 0 s
(B) alternate 1 s
(C) alternate 2 s
(D) alternate 1 s
MCQ 57
For a Z-transform
( )X z z z
z
21
31
2 65
=
b bb
l ll
Match List I (The sequences) with List II (The region of convergence ) and select the correct answer using the codes given below the lists :
List I List II
A. [( / ) ( / ) ] ( )u n1 2 1 3n n+ 1. ( / ) ( / )z1 3 1 2<
Codes :
A B C D
(A) 4 2 1 3
(B) 1 3 4 2
(C) 4 3 1 2
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(D) 1 2 4 3
MCQ 58
A system can be represented in the form of state equations as
( )S n 1+ ( ) ( )AS n Bx n= + ( )y n ( ) ( )CS n Dx n= +
Where A, B, C and D are matrices, ( )S n is the state vector. ( )x n is the input and ( )y n is the output. The transfer function of the system
( ) ( )/ ( )H z Y z X z= is given by.(A) ( )A ZI B C D1 +
(B) ( )B ZI C D A1 +
(C) ( )C ZI A B D1 +
(D) ( )D ZI A C B1 +
MCQ 59
Match List I (Fourier series and Fourier transforms) with List II (Their properties) and select the correct answer using the codes given below the lists :
List I List II
A. Fourier series 1. Discrete, periodic
B. Fourier transform 2. Continuous periodic
C. Discrete time 3. Discrete, aperiodic
D. Discrete Fourier transform 4. Continuous aperiodic
Codes :
A B C D
(A) 3 4 1 2
(B) 1 2 4 3
(C) 3 2 4 1
(D) 1 4 2 3
MCQ 60
The units of the spectrum obtained by Fourier transforming the covariance function of a stationary stochastic process is
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(A) power per Hertz
(B) energy per Hertz
(C) power per second
(D) energy per second
MCQ 61
Two independent random signals X and Y are known to be Gaussian with mean values x0 and y0 and variance andx y2 2 . A signal Z X Y= is obtained from them. The mean z0 variance . . ( )and p d f p zz2 of the signal Z are given by
(A) ,x y x y0 0 2 2+ + , Gaussian
(B) ,x y x y0 0 2 2 + + , Rayleigh
(C) ,y x y x0 0 2 2 , Uniform
(D) ,x y x y0 0 2 2 + , Gaussian
MCQ 62
If the cumulative distribution function is ( )F xx , then the probability density function ( )f xx is given as
(A) ( )F x dxx#(B) / ( )d dxF xx
(C) ( )F x dxx #(D) / ( )d dxF xx
MCQ 63
The fourier transform of e t2 is e t
2 ; then the Fourier transform of e t
2 is
(A) e1 t2
b l
(B) e t2 2
(C) e1 t2 2
(D) e 22t
MCQ 64
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Assertion (A) : The stability of the system is assured if the Region of Convergence (ROC) includes the unit circle in the Z-plane.
Reason (R) : For a causal stable system all the poles should be outside the unit circle in the Z-plane.
(A) Both A and Z are true and R is the correct explanation of A
(B) Both A and R are true but R is NOT the correct explanation of A.
(C) A is true but R is false
(D) A is false but R is true
MCQ 65
Assertion (A) : The signals ( )a u nn and ( )a u n 1n have the same Z-tranform, /( )z z a .
Reason (R) : The Reason of Convergence ( )ROC for ( )a u nn is z a>, where the ROC for ( )a u n 1n is z a< .
(A) Both A and R are true and R is the correct explanation of A
(B) Both A and R are true but R is NOT the correct explanation of A
(C) A is true but R is false
(D) A is false but R is true
MCQ 66
Assertion (A) : For a rational transfer function ( )H z to be causal, stable and causally invertible, both the zeros and the poles should lie within the unit circle in the z-plane.
Reason (R) : For a rational system, ROC bounded by poles.
(A) Both A and R are true and R is the correct explanation of A
(B) Both A and R are true but R is NOT the correct explanation of A
(C) A is true but R is false
(D) A is false but R is true
MCQ 67
Match List I (Function in the time domain) with List II (Fourier transform of the function) and select the correct answer using the
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codes given below the lists :
List I List II
A. Delta function 1. Delta function
B. Gate function 2. Gaussian function
C. Normalized Gaussion function 3. Contsant function
D. Sinusoidal function 4. Sampling function
Codes :
A B C D
(A) 1 2 4 3
(B) 3 4 2 3
(C) 1 4 2 3
(D) 3 2 4 1
MCQ 68
The poles of an analog system are related to the corresponding poles of the digital system by the relation z es= . Consider the following statements.
1. Analog system poles in the left half plane map onto digital system poles inside the circle z 1= .
2. Analog system zeros in the left half of s-plane map onto digital system zeros inside the circle z 1= .
3. Analog system poles on the imaginary axis of s-plane map onto digital system zeros on the unit circle z 1= .
Which of these statements are correct ?
(A) 1 and 2
(B) 1 and 3
(C) 3 and 4
(D) 2 and 4
MCQ 69
The range of values of a and b for which the linear time invariant system with impulse responses ( ) , ; ,h n a n b n0 0
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(B) ,a b1 1< >
(D) a b1 1>
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