This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Interpolation by a Factor I”.

1. Which of the following operation has to be performed to increase the sampling rate by an integer factor I?

a) Interpolating I+1 new samples

b) Interpolating I-1 new samples

c) Extrapolating I+1 new samples

d) Extrapolating I-1 new samples

View Answer

Explanation: An increase in the sampling rate by an integer factor of I can be accomplished by interpolating I-1 new samples between successive values of the signal.

2. In one of the interpolation process, we can preserve the spectral shape of the signal sequence x(n).

a) True

b) False

View Answer

Explanation: The interpolation process can be accomplished in a variety of ways. Among them there is a process that preserves the spectral shape of the signal sequence x(n).

3. If v(m) denote a sequence with a rate Fy=I.Fx which is obtained from x(n), then which of the following is the correct definition for v(m)?

a) x(mI), m=0,±I,±2I….

0, otherwise

a) x(mI), m=0,±I,±2I….

x(m/I), otherwise

c) x(m/I), m=0,±I,±2I….

0, otherwise

d) None of the mentioned

View Answer

Explanation: If v(m) denote a sequence with a rate Fy=I.Fx which is obtained from x(n) by adding I-1 zeros between successive values of x(n). Thus

v(m)= x(m/I), m=0,±I,±2I….

0, otherwise.

4. If X(z) is the z-transform of x(n), then what is the z-transform of interpolated signal v(m)?

a) X(zI)

b) X(z+I)

c) X(z/I)

d) X(zI)

View Answer

5. If x(m) and v(m) are the original and interpolated signals and ωy denotes the frequency variable relative to the new sampling rate, then V(ω_{y})= X(ω_{y}I).

a) True

b) False

View Answer

Explanation: The spectrum of v(m) is obtained by evaluating V(z)= X(zI) on the unit circle. Thus V(ω

_{y})= X(ω

_{y}I), where ωy denotes the frequency variable relative to the new sampling rate.

6. What is the relationship between ωx and ωy?

a) ω_{y}= ω_{x}.I

b) ω_{y}= ω_{x}/I

c) ω_{y}= ω_{x}+I

d) None of the mentioned

View Answer

Explanation: We know that the relationship between sampling rates is F

_{y}=IF

_{x}and hence the frequency variables ω

_{x}and ω

_{y}are related according to the formula

ω

_{y}= ω

_{x}/I.

7. The following sampling rate conversion technique is interpolation by a factor I.

a) True

b) False

View Answer

Explanation: From the diagram, the values are interpolated between two successive values of x(n), thus it is called as sampling rate conversion using interpolation by a factor I.

8. The following sampling rate conversion technique is interpolation by a factor I.

a) True

b) False

View Answer

Explanation: The sampling rate conversion technique given in the diagram is decimation by a factor D.

9. Which of the following is true about the interpolated signal whose spectrum is V(ω_{y})?

a) (I-1)-fold non-periodic

b) (I-1)-fold periodic repetition

c) I-fold non periodic

d) I-fold periodic repetition

View Answer

Explanation: We observe that the sampling rate increase, obtained by the addition of I-1 zero samples between successive values of x(n), results in a signal whose spectrum is a I-fold periodic repetition of the input signal spectrum.

10. C=I is the desired normalization factor.

a) True

b) False

View Answer

Explanation: The amplitude of the sampling rate converted signal should be multiplied by a factor C, whose value when equal to I is called as desired normalization factor.

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

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