June 12, 2021

Bandpass Signal Representation MCQ’s

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

1. What is the equivalent time domain relation of xl(t) i.e., lowpass signal?
a) xl(t)=[x(t)+jẋ(t)]e−j2πFct
b) x(t)+j ẋ(t) = xl(t)ej2πFct
c) xl(t)=[x(t)+jẋ(t)]e−j2πFct & x(t)+j ẋ(t) = xl(t)ej2πFct
d) None of the mentioned

2. In equation x+(t)=F−1[2V(F)]∗F−1[X(F)], if F−1[2V(F)]=δ(t)+j/πt and F−1[X(F)] = x(t). Then the value of ẋ(t) is?
a) 1π∫∞−∞x(t)t+τdτ
b) 1π∫∞−∞x(t)t−τdτ
c) 1π∫∞−∞2x(t)t−τdτ
d) 1π∫∞−∞4x(t)t−τdτ

3. 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)]

4. What is the frequency response of a Hilbert transform H(F)=?
a) ⎧⎩⎨−j(F>0)0(F=0)j(F<0)
b) ⎧⎩⎨⎪⎪−j0j(F<0)(F=0)(F>0)
c) ⎧⎩⎨⎪⎪−j0j(F>0)(F=0)(F<0)
d) ⎧⎩⎨⎪⎪j0j(F>0)(F=0)(F<0)

5. 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)]

6. If a possible representation of a band pass signal is obtained by expressing xl (t) as xl(t)=a(t)ejθ(t) then what are the equations of a(t) and θ(t)?
a) a(t) = u2c(t)+u2s(t)−−−−−−−−−−√ and θ(t)=tan−1us(t)uc(t)
b) a(t) = u2c(t)−u2s(t)−−−−−−−−−−√ and θ(t)=tan−1us(t)uc(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)}

7. What is the equivalent lowpass representation obtained by performing a frequency translation of X+(F) to Xl(F)= ?
a) X+(F+Fc)
b) X+(F-Fc)
c) X+(F*Fc)
d) X+(Fc-F)

8. 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

9. 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

10. In the relation, x(t) = uc(t)cos2πFct−us(t)sin2πFct 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

11. What is the other way of representation of bandpass signal x(t)?
a) x(t) = Re[xl(t)ej2πFct]
b) x(t) = Re[xl(t)ejπFct]
c) x(t) = Re[xl(t)ej4πFct]
d) x(t) = Re[xl(t)ej0πFct]

12. 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)

13. In the equation x(t) = Re[xl(t)ej2πFct], 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

14. If we substitute the equation xl(t)=uc(t)+jus(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)=uc(t)cos2πFct+us(t)sin2πFct; ẋ(t)=us(t)cos2πFct−uc(t)sin2πFct
b) x(t)=uc(t)cos2πFct−us(t)sin2πFct; ẋ(t)=us(t)cos2πFct+uc(t)sin2πFct
c) x(t)=uc(t)cos2πFct+us(t)sin2πFct; ẋ(t)=us(t)cos2πFct+uc(t)sin2πFct
d) x(t)=uc(t)cos2πFct−us(t)sin2πFct; ẋ(t)=us(t)cos2πFct−uc(t)sin2πFct

15. In time-domain expression, x+(t)=F−1[2V(F)]∗F−1[X(F)]. 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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