Digital Signal Processing MCQ [Free PDF] – Objective Question Answer for Digital Signal Processing Quiz

41. Sampling interval T is selected sufficiently large to completely avoid or at least minimize the effects of aliasing.

A. True
B. False

Answer: B

The digital filter with frequency response H(ω) has the frequency response characteristics of the corresponding analog filter if the sampling interval T is selected sufficiently small to completely avoid or at least minimize the effects of aliasing.

 

42. Which of the following filters cannot be designed using the impulse invariance method?

A. Low pass
B. Bandpass
C. Low and bandpass
D. High pass

Answer: D

It is clear that the impulse invariance method is inappropriate for designing high pass filters due to the spectrum aliasing that results from the sampling process.

 

43. Which of the following is the correct relation between ω and Ω?

A. Ω=ωT
B. T=Ωω
C. ω=ΩT
D. None of the mentioned

Answer: C

We know that z=esT

Now substitute s=σ+jΩ and z=r.e, which represents ‘z’ in the polar form

On equating both sides, we get

ω=ΩT.

 

44. When σ<0, then what is the condition on ‘r’?

A. 0<r<1
B. r=1
C. r>1
D. None of the mentioned

Answer: A

We know that z=esT
Now substitute s=σ+jΩ and z=r.e, which represents ‘z’ in the polar form
On equating both sides, we get
r=eσT
Thus when σ<0, the value of ‘r’ varies from 0<r<1.

 

45. When σ>0, then what is the condition on ‘r’?

A. 0<r<1
B. r=1
C. r>1
D. None of the mentioned

Answer: C

We know that z=esT

Now substitute s=σ+jΩ and z=r.e, which represents ‘z’ in the polar form
On equating both sides, we get
r=eσT

Thus when σ>0, the value of ‘r’ varies from r>1.

 

46. What is the period of the scaled spectrum Fs.X(F)?

A. 2Fs
B. Fs/2
C. 4Fs
D. Fs

Answer: D

When a continuous-time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is a periodic repetition of the scaled spectrum Fs.X(F) with period Fs.

 

47. In which of the following transformations, poles, and zeros of H(s) are mapped directly into poles and zeros in the z-plane?

A. Impulse invariance
B. Bilinear transformation
C. Approximation of derivatives
D. Matched Z-transform

Answer: D

This method of transforming an analog filter into an equivalent digital filter is to map the poles and zeros of H(s) directly into poles and zeros in the z-plane.

 

48. Which of the following is true in matched z-transform?

A. Poles of H(s) are directly mapped to poles in z-plane
B. Zeros of H(s) is directly mapped to poles in z-plane
C. Poles & Zeros of H(s) are directly mapped to poles in z-plane
D. None of the mentioned

Answer: C

In the transformation of the analog filter into the digital filter by matched z-transform method, the poles and zeros of H(s) directly into poles and zeros in the z-plane.

 

49. In matched z-transform, the poles and zeros of H(s) are directly mapped into poles and zeros in the z-plane.

A. True
B. False

Answer: A

In this method of transforming an analog filter into an equivalent digital filter is to map the poles and zeros of H(s) directly into poles and zeros in the z-plane.

 

50. The factor of the form (s-A. in H(s) is mapped into which of the following factors in the z-domain?

A. 1-eaTz
B. 1-eaTz-1
C. 1-e-aTz-1
D. 1+eaTz-1

Answer: B

If T is the sampling interval, then each factor of the form (s-A. in H(s) is mapped into the factor (1-eaTz-1) in the z-domain.

 

51. The factor of the form (s+A) in H(s) is mapped into which of the following factors in the z-domain?

A. 1-eaTz
B. 1-eaTz-1
C. 1-e-aTz-1
D. 1+eaTz-1

Answer: C

If T is the sampling interval, then each factor of the form (s+A. in H(s) is mapped into the factor (1-e-aTz-1) in the z-domain.

 

52. If the factor of the form (s-A. in H(s) is mapped into 1-eaTz-1 in the z-domain, that kind of transformation is called ______

A. Impulse invariance
B. Bilinear transformation
C. Approximation of derivatives
D. Matched Z-transform

Answer: D

If T is the sampling interval, then each factor of the form (s-A) in H(s) is mapped into the factor (1-eaTz-1) in the z-domain. This mapping is called the matched z-transform.

 

53. The poles obtained from matched z-transform are identical to poles obtained from which of the following transformations?

A. Bilinear transformation
B. Impulse invariance
C. Approximation of derivatives
D. None of the mentioned

Answer: B

The poles obtained from the matched z-transform are identical to the poles obtained with the impulse invariance method.

 

54. The zero positions obtained from matched z-transform and impulse invariance methods are not the same.

A. True
B. False

Answer: A

The poles obtained from the matched z-transform are identical to the poles obtained with the impulse invariance method. However, the two techniques result in different zero positions.

 

55. The sampling interval in the matched z-transform must be properly selected to yield the pole and zero locations at the equivalent position in the z-plane.

A. True
B. False

Answer: A

To preserve the frequency response characteristic of the analog filter, the sampling interval in the matched z-transformation must be properly selected to yield the pole and zero locations at the equivalent position in the z-plane.

 

56. What should be the value of sampling interval T, to avoid aliasing?

A. Zero
B. Sufficiently large
C. Sufficiently small
D. None of the mentioned

Answer: C

Aliasing in this matched z-transformation can be avoided by selecting the sampling interval T sufficiently small.

 

57. Low pass Butterworth filters are also called as ________

A. All-zero filter
B. All-pole filter
C. Pole-zero filter
D. None of the mentioned

Answer: B

Low pass Butterworth filters are also called all-pole filters because it has only non-zero poles.

 

58. What is the equation for the magnitude square response of a low pass Butterworth filter?

A. \(\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\)

B. \(1+(\frac{Ω}{Ω_C})^{2N}\)

C. \(\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}\)

D. None of the mentioned

Answer: A

A Butterworth is characterized by the magnitude frequency response

|H(jΩ)| = \(\frac{1}{\sqrt{1+(\frac{Ω}{Ω_C})^{2N}}}\)

where N is the order of the filter and ΩC is defined as the cutoff frequency.

 

59. What is the transfer function of magnitude squared frequency response of the normalized low pass Butterworth filter?

A. \(\frac{1}{1+(s/j)^{-2N}}\)

B. \(1+(\frac{s}{j})^{-2N}\)

C. \(1+(\frac{s}{j})^{2N}\)

D. \(\frac{1}{1+(\frac{s}{j})^{2N}}\)

Answer: D

We know that the magnitude squared frequency response of a normalized low pass Butterworth filter is given as

|H(jΩ)|2 =\(\frac{1}{1+Ω^{2N}}\)

=> HN(jΩ).HN(-jΩ)=\(\frac{1}{1+Ω^{2N}}\)

Replacing jΩ by ‘s’ and hence Ω by s/j in the above equation, we get

HN(s).HN(-s) = \(\frac{1}{1+(\frac{s}{j})^{2N}}\) which is called the transfer function.

 

60. Which of the following is the band edge value of |H(Ω)|2?

A. (1+ε2)
B. (1-ε2)
C. 1/(1+ε2)
D. 1/(1-ε2)

Answer: C

1/(1+ε2) gives the band edge value of the magnitude square response |H(Ω)|2.

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