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

1. The frequency shift can be achieved by multiplying the band pass signal as given in equation

by the quadrature carriers cos[2πF_{c}t] and sin[2πF_{c}t] and lowpass filtering the products to eliminate the signal components of 2F_{c}.

a) True

b) False

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Explanation: It is certainly be advantageous to perform a frequency shift of the band pass signal by and sampling the equivalent low pass signal. Such a frequency shift can be achieved by multiplying the band pass signal as given in the above equation by the quadrature carriers cos[2πF

_{c}t] and sin[2πF

_{c}t] and low pass filtering the products to eliminate the signal components at 2F

_{c}. Clearly, the multiplication and the subsequent filtering are first performed in the analog domain and then the outputs o f the filters are sampled.

2. What is the final result obtained by substituting F_{c}=kB-B/2 , T= 1/2B and say n = 2m i.e., for even and n=2m-1 for odd in equation

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3. Which low pass signal component occurs at the rate of B samples per second with even numbered samples of x(t)?

a) u_{c}– lowpass signal component

b) u_{s}– lowpass signal component

c) u_{c} & u_{s} – lowpass signal component

d) None of the mentioned

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Explanation: With the even-numbered samples o f x(t), which occur at the rate o f B samples per second, produce samples of the low pass signal component u

_{c}.

4. Which low pass signal component occurs at the rate of B samples per second with odd numbered samples of x(t)?

a) u_{c}– lowpass signal component

b) u_{s}– lowpass signal component

c) u_{c} & u_{s} – lowpass signal component

d) None of the mentioned

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Explanation: : With the odd-numbered samples o f x(t), which occur at the rate o f B samples per second, produce samples of the low pass signal component u

_{s}.

5. What is the reconstruction formula for the bandpass signal x(t) with samples taken at the rate of 2B samples per second?

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6. What is the new centre frequency for the increased bandwidth signal ?

a) F_{c}‘= F_{c}+B/2+B’/2

b) F_{c}‘= F_{c}+B/2-B’/2

c) F_{c}‘= F_{c}-B/2-B’/2

d) None of the mentioned

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Explanation: A new centre frequency for the increased bandwidth signal is F

_{c}‘= F

_{c}+B/2-B’/2

7. According to the sampling theorem for low pass signals with T_{1}=1/B, then what is the expression for u_{c}(t) = ?

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Explanation: To reconstruct the equivalent low pass signals. Thus, according to the sampling

theorem for low pass signals with T

_{1}= 1 / B .

8. According to the sampling theorem for low pass signals with T_{1}=1/B, then what is the expression for u_{s}(t) = ?

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Explanation: To reconstruct the equivalent low pass signals. Thus, according to the sampling

theorem for low pass signals with T

_{1}= 1 / B .

9. What is the expression for low pass signal component u_{c}(t) that can be expressed in terms of samples of the bandpass signal ?

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Explanation: The low pass signal components u

_{c}(t) can be expressed in terms of samples of the

band pass signal as follows:

10. What is the expression for low pass signal component u_{s}(t) that can be expressed in terms of samples of the bandpass signal ?

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Explanation: The low pass signal components u

_{s}(t) can be expressed in terms of samples of the

band pass signal as follows:

11. What is the Fourier transform of x(t) ?

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12. What is the basic relationship between the spectrum o f the real band pass signal x( t ) and the spectrum of the equivalent low pass signal x_{l}(t) ?

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Explanation: , where X

_{l}(F) is the Fourier transform of x

_{l}(t). This is the basic relationship between the spectrum o f the real band pass signal x ( t ) and the spectrum of the equivalent low pass signal x

_{l}(t).

**Sanfoundry Global Education & Learning Series – Digital Signal Processing.**

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