Sampling and Reconstruction of Signal MCQ [Free PDF] - Objective Question Answer for Sampling and Reconstruction of Signal Quiz

51. If we substitute the equation \(x_l (t)= u_c (t)+j u_s (t)\) in equation x (t) + j ẋ (t) = xl(t) ej2πFct and equate real and imaginary parts on side, then what are the relations that we obtain?

A. x(t)=\(u_c (t) \,cos⁡2π \,F_c \,t+u_s (t) \,sin⁡2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos⁡2π \,F_c \,t-u_c \,(t) \,sin⁡2π \,F_c \,t\)

B. x(t)=\(u_c (t) \,cos⁡2π \,F_c \,t-u_s (t) \,sin⁡2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos⁡2π \,F_c t+u_c (t) \,sin⁡2π \,F_c \,t\)

C. x(t)=\(u_c (t) \,cos⁡2π \,F_c t+u_s (t) \,sin⁡2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos⁡2π \,F_c t+u_c (t) \,sin⁡2π \,F_c \,t\)

D. x(t)=\(u_c (t) \,cos⁡2π \,F_c \,t-u_s (t) \,sin⁡2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos⁡2π \,F_c \,t-u_c (t) \,sin⁡2π \,F_c \,t\)

Answer: B

If we substitute the given equation with another, then we get the

x(t)=\(u_c (t) \,cos⁡2π \,F_c \,t-u_s (t) \,sin⁡2π \,F_c \,t\); ẋ(t)=\(u_s (t) \,cos⁡2π \,F_c t+u_c (t) \,sin⁡2π \,F_c \,t\)

52. In the relation, x(t) = \(u_c (t) cos⁡2π \,F_c \,t-u_s (t) sin⁡2π \,F_c \,t\) the low frequency components uc and us are called _____ of the bandpass signal x(t).

A. Quadratic components
B. Quadrature components
C. Triplet components
D. None of the mentioned

Answer: B

The low-frequency signal components uc(t) and us(t) can be viewed as amplitude modulations impressed on the carrier components cos2πFct and sin2πFct, respectively. Since these carrier components are in phase quadrature, uc(t) and us(t) are called the Quadrature components of the bandpass signal x (t).

53. What is the other way of representing of bandpass signal x(t)?

A. x(t) = Re\([x_l (t) e^{j2πF_c t}]\)

B. x(t) = Re\([x_l (t) e^{jπF_c t}]\)

C. x(t) = Re\([x_l (t) e^{j4πF_c t}]\)

D. x(t) = Re\([x_l (t) e^{j0πF_c t}]\)

Answer: A

The above signal is formed from quadrature components of bandpass signal x(t) is

= Re\([x_l (t) e^{j2πF_c t}]\)

where Re denotes the real part of complex valued quantity.

54. In the equation x(t) = Re\([x_l (t) e^{j2πF_c t}]\), What is the lowpass signal xl (t) is usually called the ___ of the real signal x(t).

A. Mediature envelope
B. Complex envelope
C. Equivalent envelope
D. All of the mentioned

Answer: B

In the equation x(t) = Re[xl(t)e(j2πFct)], Re denotes the real part of the complex-valued quantity in the brackets following. The lowpass signal xl (t) is usually called the Complex envelope of the real signal x(t), and is basically the equivalent low pass signal.

55. If a possible representation of a band pass signal is obtained by expressing xl (t) as \(x_l (t)=a(t)e^{jθ(t})\) then what are the equations of a(t) and θ(t)?

A. a(t) = \(\sqrt{u_c^2 (t)+u_s^2 (t)}\) and θ(t)=\(tan^{-1}\frac{u_s (t)}{u_c (t)}\)

B. a(t) = \(\sqrt{u_c^2 (t)-u_s^2 (t)}\) and θ(t)=\(tan^{-1}\frac{u_s (t)}{u_c (t)}\)

C. a(t) = \(\sqrt{u_c^2 (t)+u_s^2 (t)}\) and θ(t)=\(tan^{-1}\frac{u_c (t)}{u_s (t)}\)

D. a(t) = \(\sqrt{u_s^2 (t)-u_c^2 (t)}\) and θ(t)=\(tan^{-1}⁡\frac{u_s (t)}{u_c (t)}\)

Answer: A

A third possible representation of a band pass signal is obtained by expressing \(x_l (t)=a(t)e^{jθ(t)}\) where a(t) = \(\sqrt{u_c^2 (t)+u_s^2 (t)}\) and θ(t)=\(tan^{-1}\frac{u_s (t)}{u_c (t)}\).

56. What is the possible representation of x(t) if xl(t)=a(t)e(jθ(t))?

A. x(t) = a(t) cos[2πFct – θ(t)]
B. x(t) = a(t) cos[2πFct + θ(t)]
C. x(t) = a(t) sin[2πFct + θ(t)]
D. x(t) = a(t) sin[2πFct – θ(t)]

Answer: B

x(t) = Re\([x_l (t) e^{j2πF_c t}]\)

= Re\([a(t) e^{j[2πF_c t + θ(t)]}]\)

= \(a(t) \,cos⁡ [2πF_c t+θ(t)]\)

Hence proved.

57. In the equation x(t) = a(t)cos[2πFct+θ(t)], Which of the following relations between a(t) and x(t), θ(t) and x(t) are true?

A. a(t), θ(t) are called the Phases of x(t)
B. a(t) is the Phase of x(t), θ(t) is called the Envelope of x(t)
C. a(t) is the Envelope of x(t), θ(t) is called the Phase of x(t)
D. none of the mentioned

Answer: C

In the equation x(t) = a(t) cos[2πFct+θ(t)], the signal a(t) is called the Envelope of x(t), and θ(t) is called the phase of x(t).

58. The basic task of the A/D converter is to convert a discrete set of digital code words into a continuous range of input amplitudes.

A. True
B. False

Answer: B

The basic task of the A/D converter is to convert a continuous range of input amplitude into a discrete set of digital code words. This conversion involves the processes of Quantization and Coding.

59. What is the type of quantizer, if a Zero is assigned a quantization level?

A. Midrise type
B. Mid tread type
C. Mistreat type
D. None of the mentioned

Answer: C

If a zero is assigned a quantization level, the quantizer is of the Mid-tread type.

The Mid-tread type is so-called because the origin lies in the middle of a tread of the stair-case-like graph. The quantization levels in this type are odd in number.

60. What is the type of quantizer, if a Zero is assigned a decision level?

A. Midrise type
B. Mid tread type
C. Mistreat type
D. None of the mentioned

Answer: A

If a zero is assigned a decision level, the quantizer is of the midrise type.

The Mid-Rise type is so-called because the origin lies in the middle of a raising part of the stair-case-like graph.

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