250+ TOP MCQs on Interpolation by a Factor I & Answers

Digital Signal Processing Multiple Choice Questions 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
Answer: B
Clarification: 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
Answer: A
Clarification: 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 F_y=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

B.

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
Answer: C
Clarification: If v(m) denote a sequence with a rate F_y=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)
Answer: D
Clarification: By taking the z-transform of the signal v(m), we get
V(z)=(sum_{m=-∞}^∞ v(m)z^{-m})
=(sum_{m=-∞}^∞ x(m)z^{-mI})
= X(z^-I)

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_yI).
A. True
B. False
Answer: A
Clarification: The spectrum of v(m) is obtained by evaluating V(z) = X(z^I) on the unit circle. Thus V(ω_y)= X(ω_yI), where ωy denotes the frequency variable relative to the new sampling rate.

6. What is the relationship between ω_x and ω_y?
A. ω_y= ω_x.I
B. ω_y= ω_x/I
C. ω_y= ω_x+I
D. None of the mentioned
Answer: B
Clarification: 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
Answer: A
Clarification: 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
Answer: B
Clarification: 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
Answer: D
Clarification: 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 an I-fold periodic repetition of the input signal spectrum.

10. C=I is the desired normalization factor.
A. True
B. False
Answer: A
Clarification: 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.