## [MCQ] Signals and Systems

Exit Intent

#### Module 2

1. Impulse response is the output of ______ system due to impulse input applied at time=0?
a) Linear
b) Time-varying
c) Time invariant
d) Linear and time-invariant

2. Which of the following is correct regarding to impulse signal?
a) x[n]δ[n] = x[0]δ[n]
b) x[n]δ[n] = δ[n]
c) x[n]δ[n] = x[n]
d) x[n]δ[n] = x[0]

3. Weighted superposition of time-shifted impulse responses is termed as _______ for discrete-time signals.
a) Convolution integral
b) Convolution multiple
c) Convolution sum
d) Convolution

4. Which of the following is a correct expression for Impulse response?

5. Determine the output of a LTI system,

a)
b)
c)
d)

6. Determine the output of LTI system to

a)
b)
c)
d)

7. Find the convolution sum of sequences x1[n] = (1, 2, 3) and x2[n] = (2, 1, 4).
a) {2, 5, 12, 11, 12}
b) {2, 12, 5, 11, 12}
c) {2, 11, 5, 12, 12}
d) {-2, 5,-12, 11, 12}

8. Find the convolution sum of sequence x1[n] = {1, 2, 3} and

9. Determine the output of LTI with input x[n] =2δ(n)-δ(n-1) and h[n] given as below.

10. Consider h [n] as in figure 1 and x[n] = u[n] – u [n-3], determine the output y [n] of the LTI system?

11. The convolution sum is given by _____ equation.

12. When the sequences x1 [n] = u [n] and x2 [n] = u [n-3], the output of LTI system is given as _____
a) y[n] = n-2, n>3
b) y[n] = n-2, n≥3
c) y[n] = n+2, n>3
d) y[n] = n-2, n≤3

14. Is (t)*h(t) = h(t)*x(t)?
a) True
b) False

15. Compute u (t) convolved with itself?
a) y(t)=t.u(t)
b) y(t)=u(t)
c) y(t)=t2.u(t)
d) y(t)=t.u(t-1)

17. Convolve graphically.

a)
b)
c)
d)

18. Convolve graphically the below given signals, and determine the correct sequence?

a) Y (-1) = 0, y (1) = 2, y (3) = 2
b) Y (-1) = 2, y (1) = 2, y (3) = 2
c) Y (-1) = 0, y (1) = 0, y (3) = 2
d) Y (-1) = 0, y (1) = 3, y (3) = 2

19. Convolve given x (t) with itself and choose the correct output.

a)
b)
c)
d)

20. Find the convolution of x1[n] = {1, 2, 3, 4} and x2[n] = {2, 1, 2, 1}.
a) Y[n] = {14, 10, 14, 10}
b) Y [n] = {14, 16, 14, 16}
c) Y [n] = {14, 16,-14,-16}
d) Y [n] = {14,-16,-14, 16}

21. If two LTI systems with impulse response h1 (t) and h2 (t) and are connected in parallel then output is given by ______
a) y(t) = x(t) *(h1(t) + h2(t))
b) y(t) = x(t) + (h1(t) + h2(t))
c) y(t) = x(t) * (h1(t) h2(t))
d) y(t) = (x(t) * h1(t)) + h2(t)

22. When two LTI systems with impulse responses ha (t) and hb (t) are cascaded then equivalent response is given by ______
a) h(t) = ha(t) + hb(t)
b) h(t) = ha(t) – hb(t)
c) h(t) = ha(t) hb(t)
d) h(t) = ha(t) * hb(t)

23. What is this property of impulse response is called ___________
h1(t) * h2(t) = h2(t) * h1(t)
a) Associative property
b) Commutative property
c) Distributive property
d) Closure law

24. The overall impulse response of the system is given by ______

a) h(t) = (h1(t) + h2(t) * h3(t)) – h4(t)
b) y(t) = x(t) * (h1(t) + h2(t)*h3(t)) – h4(t)
c) h(t) = (h1(t) + h2(t) * h3(t)) + h4(t) * x(t)
d) h(t) = (h1(t) h2(t) * h3(t)) – h4(t)

25. The overall impulse response of the system is given by ______

a) h[n] = (h1[n]-h2[n])*h3[n]+h5[n]*h4[n]
b) h[n] = (((h1[n]-h2[n])*h3[n])+h5[n])*h4[n]
c) h[n] = (((h1[n]-h2[n])*h3[n])-h5[n])*h4[n]
d) h[n] = (((h1[n]-h2[n])*-h3[n])-h5[n])*h4[n]

26. The condition for memory-less system is given by _____
a) h[k] = cδ[k]
b) h[k] = cδ[n-k]
c) h[k] = ch[k]δ[k]
d) h[k] = ch[n-k]δ[k]

27. The causal continuous system with impulse response should satisfy ____ equation.
a) h(t)=0,t<0
b) h(t)=0,t>0
c) h(t)≠0,t<0
d) h(t)≠0,t≤0

28. Causal systems are ______
a) Anticipative
b) Non anticipative
c) For certain cases anticipative
d) For certain cases anticipative and non anticipative

29. Which of the following is true for discrete-time stable systems?

30. The impulse response of discrete-time signal is given by h [n] = u [n+3]. Whether the system is causal or not?
a) Causal
b) Non-causal
c) Insufficient information
d) The system cannot be classified

31. What is the rule h*(x+y) = (y+x)*h called?
a) Commutativity rule
b) Associativity rule
c) Distributive rule
d) Transitive rule

32. Does the system h(t) = exp([-1-2j]t) correspond to a stable system?
a) Yes
b) No
c) Marginally Stable
d) None of the mentioned

33. What is the rule h*(x*c) = (x*h)*c called?
a) Commutativity rule
b) Associativity rule
c) Distributive rule
d) Associativity and Commutativity rule

34. Is y[n] = n*cos(n*pi/4)u[n] a stable system?
a) Yes
b) No
c) Marginally stable
d) None of the mentioned

35. What is the rule (h*x)*c = h*(x*c) called?
a) Commutativity rule
b) Associativity rule
c) Distributive rule
d) Transitive rule

36. Is y[n] = n*sin(n*pi/4)u[-n] a stable system?
a) Yes
b) No
c) Marginally stable
d) None of the mentioned

37. What is the following expression equal to: h*(c*(b+d(t))), d(t) is the delta function
a) h*c + h*b
b) h*c*b + b
c) h*c*b + h*c
d) h*c*b + h

38. Does the system h(t) = exp([1-4j]t) correspond to a stable system?
a) Yes
b) No
c) Marginally Stable
d) None of the mentioned

39. The system transfer function and the input if exchanged will still give the same response.
a) True
b) False

40. For an LTI discrete system to be stable, the square sum of the impulse response should be
a) Integral multiple of 2pi
b) Infinity
c) Finite
d) Zero

41. Is discrete time convolution possible?
a) True
b) False

42. How is discrete time convolution represented?
a) x[n] + h[n]
b) x[n] – h[n]
c) x[n] * h[n]
d) x[n] + h[n]

43. What are the tools used in a graphical method of finding convolution of discrete time signals?
a) Plotting, shifting, folding, multiplication, and addition in order
b) Scaling, shifting, multiplication, and addition in order
c) Scaling, multiplication and addition in order
d) Scaling, plotting, shifting, multiplication and addition in order

44. Choose the correct equation for finding the output of a discrete time convolution?
a) y[n] = ∑x[k]h[n-k], k from 0 to ∞
b) y[n] = ∑x[k]h[n-k], k from -∞ to +∞
c) y[n] = ∑x[k]h[k], k from 0 to ∞
d) y[n] = ∑x[k]h[n], k from -∞ to +∞

45. What is a convolution sum?
a) ∑x[k]h[n-k], k from -∞ to +∞
b) ∑x[k]*∑h[n-k], k from -∞ to +∞
c) ∑x[k]+∑h[n-k], k from -∞ to +∞
d) ∑∑x[k]h[n-k], k from -∞ to +∞

47. Choose the properties which are followed by a discrete time convolution?
a) Associative, commutative, distributive
b) Associative
c) Commutative and distributive
d) Distributive and associative

48. What is the convolution of a signal with an impulse?
a) Signal itself
b) Impulse
c) A new signal
d) Signal multiplied by impulse

49. What is the commutative property?
a) x(n)*h(n)=h(n)*x(n)
b) x(n)+h(n)=h(n)+x(n)
c) x(n)**h(n)=h(n)**x(n)
d) x(n)h(n)=h(n)x(n)

50. What is the associative property of discrete time convolution?
a) [x1(n) * x2(n)]*h(n) = x1(n)* [x2(n)*h(n)]
b) [x1(n) * x2(n)]+h(n) = x1(n) + [x2(n)*h(n)]
c) [x1(n) + x2(n)]*h(n) = x1(n)* [x2(n)+h(n)]
d) [x1(n) * x2(n)]h(n) = x1(n) [x2(n)*h(n)]

51. What is the rule h*x = x*h called?
a) Commutativity rule
b) Associativity rule
c) Distributive rule
d) Transitive rule

52. For an LTI discrete system to be stable, the square sum of the impulse response should be
a) Integral multiple of 2pi
b) Infinity
c) Finite
d) Zero

53. What is the rule (h*x)*c = h*(x*c) called?
a) Commutativity rule
b) Associativity rule
c) Distributive rule
d) Transitive rule

54. Does the system h(t) = exp(-7t) correspond to a stable system?
a) Yes
b) No
c) Marginally Stable
d) None of the mentioned

55. What is the following expression equal to: h*(d+bd), d(t) is the delta function
a) h + d
b) b + d
c) d
d) h + b

56. Does the system h(t) = exp([14j]t) correspond to a stable system?
a) Yes
b) No
c) Marginally Stable
d) None of the mentioned

57. What is the rule c*(x*h) = (x*h)*c called?
a) Commutativity rule
b) Associativity rule
c) Distributive rule
d) Associativity and Commutativity rule

58. Is y[n] = n*sin(n*pi/4)u[-n] a causal system?
a) Yes
b) No
c) Marginally causal
d) None of the mentioned

59. The system transfer function and the input if exchanged will still give the same response.
a) True
b) False

60. Is y[n] = nu[n] a linear system?
a) Yes
b) No

#### Module 3

1. Impulse response is the output of ______ system due to impulse input applied at time=0?
a) Linear
b) Time varying
c) Time invariant
d) Linear and time invariant

2. Which of the following is correct regarding to impulse signal?
a) x[n]δ[n] = x[0]δ[n]
b) x[n]δ[n] = δ[n]
c) x[n]δ[n] = x[n]
d) x[n]δ[n] = x[0]

3. Weighted superposition of time-shifted impulse responses is termed as _______ for discrete-time signals.
a) Convolution integral
b) Convolution multiple
c) Convolution sum
d) Convolution

4. Which of the following is a correct expression for Impulse response?

5. Determine the output of a LTI system,
a)
b)
c)
d)

6. Determine the output of LTI system to
a)
b)
c)
d)

7. Find the convolution sum of sequences x1[n] = (1, 2, 3) and x2[n] = (2, 1, 4).
a) {2, 5, 12, 11, 12}
b) {2, 12, 5, 11, 12}
c) {2, 11, 5, 12, 12}
d) {-2, 5,-12, 11, 12}

8. Find the convolution sum of sequence x1[n] = {1, 2, 3} and

9. Determine the output of LTI with input x[n] =2δ(n)-δ(n-1) and h[n] given as below.

10. Consider h [n] as in figure 1 and x[n] = u[n] – u [n-3], determine the output y [n] of the LTI system?

12. The Fourier series of the given signal is _______________

a) -4/π sin x
b) 4/π sin x
c) 4/π cos x
d) -4/π cos x

13. For the circuit given below, the effective inductance of the circuit across the terminal AB, is ___________

a) 9 H
b) 21 H
c) 11 H
d) 6 H

14. For the circuit given below, the inductance measured across the terminals 1 and 2 was 15 H with open terminals 3 and 4. It was 30 H when terminals 3 and 4 were short-circuited. Both the inductors are having inductances 2H. The coefficient of coupling is ______________

a) 1
b) 0.707
c) 0.5
d) Inderminate due to insufficient data

15. In the circuit given below, the resonant frequency is ________________

16. Q meter operator is the principle of __________
a) Series resonance
b) Current resonance
c) Self-inductance
d) Eddy currents

17. The probability cumulative distribution function must be monotone as well as ___________
a) Increasing
b) Decreasing
c) Non-increasing
d) Non-decreasing

18. The impedance seen by the source in the circuit is given by __________

a) (0.54 + j0.313) Ω
b) (4 – j2) Ω
c) (4.54 – j1.69) Ω
d) (4 + j2) Ω

19. In the circuit given below, the capacitor is initially having a charge of 10 C. 1 second after the switch is closed, the current in the circuit is ________

a) 14.7 A
b) 18.5 A
c) 40.0 A
d) 50.0 A

20. Convolution is used to find ____________
a) Impulse of an LTI system
b) Frequency response of an LTI system
c) Time response of an LTI system
d) Phase response of an LTI system

21. The Fourier transform of a rectangular function is ___________
a) Another rectangular pulse
b) Triangular pulse
c) Sinc function
d) Impulse

22. The property of Fourier Transform which states that the compression in time domain is equivalent to expansion in the frequency domain is ___________
a) Duality
b) Scaling
c) Time scaling
d) Frequency shifting

23. A coil of inductance 10 H, resistance 40 Ω is connected as shown in the figure. After the switch S has been in connection with point 1 for a very long time, it is moved to point 2 at t=0. For the value of R obtained, the time taken for 95 % of the stored energy dissipated is close to?

a) 0.10 s
b) 0.15 s
c) 0.50 s
d) 1.0 s

24. The function which has its Fourier transform, Laplace transform, and Z transform unity is __________
a) Gaussian
b) Impulse
c) Sinc
d) Pulse

38. The Fourier transform of a Gaussian pulse is also a Gaussian pulse.
a) True
b) False

42. Find the Fourier transform of x(t) = f(t – 2) + f(t + 2).
a) 2F(ω)cos⁡2ω
b) F(ω)cos⁡2ω
c) 2F(ω)sin⁡2ω
d) F(ω)sin⁡2ω

#### Module 4

3. Find the Laplace transform of δ(t).
a) 1
b) 0
c) ∞
d) 2

52. For the system, y (t) = u{x (t)} which of the following holds true?
a) System is Linear, time-invariant, causal and stable
b) System is time-invariant, causal and stable
c) System is causal and stable
d) System is stable

53. Given, R = 10 Ω, L = 100 mH and C = 10 μF. Selectivity is ____________

a) 10
b) 1.2
c) 0.15
d) 0.1

54. For the circuit given below, if the frequency of the source is 50 Hz, then a value of to which results in a transient free response is _________________

a) 0
b) 1.78 ms
c) 7.23 ms
d) 9.21 ms

55. A series RC circuit excited by voltage V is __________
a) A memory less system
b) A causal system
c) A dynamic system
d) Static system

#### Module 5

1. When do DTFT and ZT are equal?
a) When σ = 0
b) When r = 1
c) When σ = 1
d) When r = 0

5. For causal sequences, the ROC is the exterior of a circle of radius r.
a) True
b) False

10. For a right hand sequence, the ROC is entire z-plane.
a) True
b) False

#### Module 6

1. If M and N are the orders of numerator and denominator of rational system function respectively, then how many multiplications are required in direct form-I realization of that IIR filter?
a) M+N-1
b) M+N
c) M+N+1
d) M+N+2

2. If M and N are the orders of numerator and denominator of rational system function respectively, then how many additions are required in direct form-I realization of that IIR filter?
a) M+N-1
b) M+N
c) M+N+1
d) M+N+2

3. If M and N are the orders of numerator and denominator of rational system function respectively, then how many memory locations are required in direct form-I realization of that IIR filter?
a) M+N+1
b) M+N
c) M+N-1
d) M+N-2

4. In direct form-I realization, all-pole system is placed before the all-zero system.
a) True
b) False

5. If M and N are the orders of numerator and denominator of rational system function respectively, then how many memory locations are required in direct form-II realization of that IIR filter?
a) M+N+1
b) M+N
c) Min [M,N]
d) Max [M,N]

6. The basic elements of a flow graph are branches and nodes.
a) True
b) False

7. Which of the following is true for the given signal flow graph?

a) Two pole system
b) Two zero system
c) Two pole and two zero system
d) None of the mentioned

8. What are the nodes that replace the adders in the signal flow graphs?
a) Source node
b) Sink node
c) Branch node
d) Summing node

9. The output signal of a system is extracted at a sink node.
a) True
b) False

10. If we reverse the directions of all branch transmittances and interchange the input and output in the flow graph, then the resulting structure is called as ______________
a) Direct form-I
b) Transposed form
c) Direct form-II
d) None of the mentioned

11. What does the structure given below represents?

a) Direct form-I
b) Regular Direct form-II
c) Transposed direct form-II
d) None of the mentioned

12. The structure shown below is known as ____________

a) Parallel form structure
c) Direct form
d) None of the mentioned

13. Which of the following is an method for implementing an FIR system?
a) Direct form
c) Lattice structure
d) All of the mentioned

14. How many memory locations are used for storage of the output point of a sequence of length M in direct form realization?
a) M+1
b) M
c) M-1
d) None of the mentioned

15. The direct form realization is often called a transversal or tapped-delay-line filter.
a) True
b) False

16. What is the condition of M, if the structure according to the direct form is as follows?

a) M even
b) M odd
c) All values of M
d) Doesn’t depend on value of M

17. By combining two pairs of poles to form a fourth order filter section, by what factor we have reduced the number of multiplications?
a) 25%
b) 30%
c) 40%
d) 50%

19. The realization of FIR filter by frequency sampling realization can be viewed as cascade of how many filters?
a) Two
b) Three
c) Four
d) None of the mentioned

21. The zeros of the system function of comb filter are located at ______________
a) Inside unit circle
b) On unit circle
c) Outside unit circle
d) None of the mentioned

24. When the desired frequency response characteristic of the FIR filter is narrowband, most of the gain parameters {H(k+α)} are zero.
a) True
b) False

25. Which of the following filters have a cascade realization as shown below?

a) IIR filter
b) Comb filter
c) High pass filter
d) FIR filter