ies - electronics engineering - signals and systems

IES E & T Topic wise QuestionsSignal & Systems

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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

IES E & T Topic wise 1999-2009 Signal & Systems

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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

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



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



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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