Band Pass Signal Sampling MCQ’s

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Band Pass Signal Sampling”.

1. What is the reconstruction formula for the bandpass signal x(t) with samples taken at the rate of 2B samples per second?
a) ∑∞m=−∞x(mT)sin(π/2T)(t−mT)(π/2T)(t−mT)cos2πFc(t−mT)
b) ∑∞m=−∞x(mT)sin(π/2T)(t+mT)(π/2T)(t+mT)cos2πFc(t−mT)
c) ∑∞m=−∞x(mT)sin(π/2T)(t−mT)(π/2T)(t−mT)cos2πFc(t+mT)
d) ∑∞m=−∞x(mT)sin(π/2T)(t+mT)(π/2T)(t+mT)cos2πFc(t+mT)

2. What is the expression for low pass signal component uc(t) that can be expressed in terms of samples of the bandpass signal?
a) ∑∞n=−∞(−1)n+r+1x(2nT‘−T‘)sin(π/(2T‘))(t−2nT‘+T‘)(π/(2T‘))(t−2nT‘+T‘)
b) ∑∞n=−∞(−1)nx(2nT‘)sin(π/(2T‘))(t−2nT‘)(π/(2T‘))(t−2nT‘)
c) All of the mentioned
d) None of the mentioned

3. Which low pass signal component occurs at the rate of B samples per second with odd numbered samples of x(t)?
a) uc – lowpass signal component
b) us – lowpass signal component
c) uc & us – lowpass signal component
d) none of the mentioned

4. What is the Fourier transform of x(t)?
a) X (F) = 12[Xl(F−Fc)+X∗l(F−Fc)]b) X (F) = 12[Xl(F−Fc)+X∗l(F+Fc)]c) X (F) = 12[Xl(F+Fc)+X∗l(F−Fc)]d) X (F) = 12[Xl(F−Fc)+X∗l(−F−Fc)]

5. What is the new centre frequency for the increased bandwidth signal?
a) Fc‘= Fc+B/2+B’/2
b) Fc‘= Fc+B/2-B’/2
c) Fc‘= Fc-B/2-B’/2
d) None of the mentioned

6. Which low pass signal component occurs at the rate of B samples per second with even numbered samples of x(t)?
a) uc-lowpass signal component
b) us-lowpass signal component
c) uc & us-lowpass signal component
d) none of the mentioned

7. According to the sampling theorem for low pass signals with T1=1/B, then what is the expression for us(t) = ?
a) ∑∞m=−∞uc(mT1)sin(πT1)(t−mT1)(πT1)(t−mT1)
b) ∑∞m=−∞us(mT1−T12)sin(πT1)(t−mT1+T12)(π/T1)(t−mT1+T12)
c) ∑∞m=−∞us(mT1−T12)sin(πT1)(t−mT1−T12)(πT1)(t−mT1−T12)
d) ∑∞m=−∞uc(mT1)sin(πT1)(t+mT1)(πT1)(t+mT1)

8. The frequency shift can be achieved by multiplying the band pass signal as given in equation
x(t) = uc(t)cos2πFct−us(t)sin2πFct by the quadrature carriers cos[2πFct] and sin[2πFct] and lowpass filtering the products to eliminate the signal components of 2Fc.
a) True
b) False

9. What is the expression for low pass signal component us(t) that can be expressed in terms of samples of the bandpass signal?
a) ∑∞n=−∞(−1)n+r+1x(2nT‘−T‘)sin(π/(2T‘))(t−2nT‘+T‘)(π/(2T‘))(t−2nT‘+T‘)
b) ∑∞n=−∞(−1)nx(2nT‘)sin(π/(2T‘))(t−2nT‘)(π/(2T‘))(t−2nT‘)
c) All of the mentioned
d) None of the mentioned

10. According to the sampling theorem for low pass signals with T1=1/B, then what is the expression for uc(t) = ?
a) ∑∞m=−∞uc(mT1)sin(πT1)(t−mT1)(π/T1)(t−mT1)
b) ∑∞m=−∞us(mT1−T12)sin(πT1)(t−mT1+T1/2)(πT1)(t−mT1+T12)
c) ∑∞m=−∞uc(mT1)sin(πT1)(t+mT1)(πT1)(t+mT1)
d) ∑∞m=−∞us(mT1−T12)sin(πT1)(t+mT1+T12)(πT1)(t+mT1+T12)

11. What is the basic relationship between the spectrum of the real bandpass signal x(t) and the spectrum of the equivalent low pass signal xl(t)?
a) X (F) = 12[Xl(F−Fc)+X∗l(F−Fc)]b) X (F) = 12[Xl(F−Fc)+X∗l(F+Fc)]c) X (F) = 12[Xl(F+Fc)+X∗l(F−Fc)]d) X (F) = 12[Xl(F−Fc)+X∗l(−F−Fc)]

12. What is the final result obtained by substituting Fc=kB-B/2, T= 1/2B and say n = 2m i.e., for even and n=2m-1 for odd in equation x(nT)= uc(nT)cos2πFcnT−us(nT)sin2πFcnT?
a) (−1)muc(mT1)−us
b) us(mT1−T12)(−1)m+k+1
c) None
d) (−1)muc(mT1)−us(mT1−T12)(−1)m+k+1

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