This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “The Representation of Bandpass Signals”.

1. Which of the following is the right way of representation of equation that contains only the positive frequencies in a given x(t) signal?

a) X_{+}(F)=4V(F)X(F)

b) X_{+}(F)=V(F)X(F)

c) X_{+}(F)=2V(F)X(F)

d) X_{+}(F)=8V(F)X(F)

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Explanation: In a real valued signal x(t), has a frequency content concentrated in a narrow band of frequencies in the vicinity of a frequency F

_{c}. Such a signal which has only positive frequencies can be expressed as X

_{+}(F)=2V(F)X(F)

Where X

_{+}(F) is a Fourier transform of x(t) and V(F) is unit step function.

2. What is the equivalent time –domain expression of X_{+}(F)=2V(F)X(F)?

a) F^{(+1)}2V(F)*F^{(+1)}X(F)

b) F^{(-1)}4V(F)*F^{(-1)}X(F)

c) F^{(-1)}V(F)*F^{(-1)}X(F)

d) F^{(-1)}2V(F)*F^{(-1)}X(F)

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3. In time-domain expression, The signal x_{+}(t) is known as

a) Systematic signal

b) Analytic signal

c) Pre-envelope of x(t)

d) Both Analytic signal & Pre-envelope of x(t)

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4. In equation

Then the value of ẋ(t) is ?

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5. If the signal ẋ(t) can be viewed as the output of the filter with impulse response h(t) = 1/πt , -∞ < t < ∞

when excited by the input signal x(t) then such a filter is called as___

a) Analytic transformer

b) Hilbert transformer

c) Both Analytic & Hilbert transformer

d) None of the mentioned

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Explanation: The signal ẋ(t) can be viewed as the output of the filter with impulse response h(t) = 1/πt ,

-∞ < t < ∞ when excited by the input signal x(t) then such a filter is called as Hilbert transformer.

6. What is the frequency response of a Hilbert transform H(F)=?

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Explanation:

We Observe that │H (F) │=1 and the phase response ʘ(F) = -1/2π for F > 0 and ʘ(F) = 1/2π for F < 0.

7. What is the equivalent lowpass representation obtained by performing a frequency translation of X_{+}(F) to X_{l}(F)= ?

a) X_{+}(F+F_{c})

b) X_{+}(F-F_{c})

c) X_{+}(F*F_{c})

d) X_{+}(F_{c}-F)

View Answer

Explanation: The analytic signal x

_{+}(t) is a bandpass signal. We obtain an equivalent lowpass representation by performing a frequency translation of X

_{+}(F).

8. What is the equivalent time domain relation of x_{l}(t) i.e., lowpass signal?

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9. If we substitute the equation in equation x (t) +j ẋ (t) = x_{l}(t) e^{(j2πFct)} and equate real and imaginary parts on side, then what are the relations that we obtain?

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Explanation: If we substitute the given equation in other, then we get the required result

10. In the relation, the low frequency components u_{c} and u_{s} are called __ of the bandpass signal x(t).

a) Quadratic components

b) Quadrature components

c) Triplet components

d) None of the mentioned

View Answer

Explanation: The low -frequency signal components u

_{c}(t) and u

_{s}(t) can be viewed as amplitude modulations impressed on the carrier components cos2πF

_{c}t and sin2πF

_{c}t , respectively. Since these carrier components are in phase quadrature, u

_{c}(t) and u

_{s}(t) are called the Quadrature components of the bandpass signal x (t).

11. What is the other way of representation of bandpass signal x(t)?

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Explanation: The above signal is formed from quadrature components, where Re denotes the real part of complex valued quantity.

12. In the equation What is the lowpass signal x_{l} (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

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Explanation: In the equation x(t) = Re[x

_{l}(t)e

^{(j2πFct)}],Re denotes the real part of the complex valued quantity in the brackets following. The lowpass signal x_l (t) is usually called the Complex envelope of the real signal x(t) , and is basically the equivalent low pass signal.

13. If a possible representation of a band pass signal is obtained by expressing x_{l} (t) as then what are the equations of a(t) and θ(t) ?

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Explanation: A third possible representation of a band pass signal is obtained by expressing

14. What is the possible representation of x(t) if x_{l}(t)=a(t)e^{(jθ(t))} ?

a) x(t) = a(t) cos(2pF_{c}t – ?(t))

b) x(t) = a(t) cos(2pF_{c}t + ?(t))

c) x(t) = a(t) sin(2pF_{c}t + ?(t))

d) x(t) = a(t) sin(2pF_{c}t – ?(t))

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15. In the equation x(t) = a(t)cos[2πF_{c}t+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

View Answer

Explanation: In the equation x(t) = a(t) cos[2πF

_{c}t+θ(t) ], the signal a(t) is called the Envelope of x(t), and θ(t) is called the phase of x(t)

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