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

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

A. True

B. False

3. If v(m) denotes 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

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

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)

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(ωy)= X(ωyI).

A. True

B. False

6. What is the relationship between ωx and ωy?

A. ωy= ωx.I

B. ωy= ωx/I

C. ωy= ωx+I

D. None of the mentioned

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

A. True

B. False

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

A. True

B. False

9. Which of the following is true about the interpolated signal whose spectrum is V(ωy)?

A. (I-1)-fold non-periodic

B. (I-1)-fold periodic repetition

C. I-fold non periodic

D. I-fold periodic repetition

10. C=I is the desired normalization factor.

A. True

B. False

11. Sampling rate conversion by the rational factor I/D is accomplished by what connection of interpolator and decimator?

A. Parallel

B. Cascade

C. Convolution

D. None of the mentioned

12. Which of the following has to be performed in sampling rate conversion by rational factor?

A. Interpolation

B. Decimation

C. Either interpolation or decimation

D. None of the mentioned

13. Which of the following operation is performed by the blocks given in the figure below?

A. Sampling rate conversion by a factor I

B. Sampling rate conversion by a factor D

C. Sampling rate conversion by a factor D/I

D. Sampling rate conversion by a factor I/D

14. The Nth root of unity WN is given as ______

A. e^{j2πN}

B. e^{-j2πN}

C. e^{-j2π/N}

D. e^{j2π/N}

15. Which of the following is true regarding the number of computations requires to compute an N-point DFT?

A. N2 complex multiplications and N(N-1) complex additions

B. N2 complex additions and N(N-1) complex multiplications

C. N2 complex multiplications and N(N+1) complex additions

D. N2 complex additions and N(N+1) complex multiplications

16. Which of the following is true?

A. \(W_N^*=\frac{1}{N} W_{N^{-1}}\)

B. \(W_N-1=\frac{1}{N} W_{N^*}\)

C. \(W_N-1=W_{N^*}\)

D. None of the mentioned

17. What is the DFT of the four point sequence x(n)={0,1,2,3}?

A. {6,-2+2j-2,-2-2j}

B. {6,-2-2j,2,-2+2j}

C. {6,-2+2j,-2,-2-2j}

D. {6,-2-2j,-2,-2+2j}

18. If X(k) is the N point DFT of a sequence whose Fourier series coefficients is given by ck, then which of the following is true?

A. X(k)=Nck

B. X(k)=ck/N

C. X(k)=N/ck

D. None of the mentioned

19. What is the DFT of the four point sequence x(n)={0,1,2,3}?

A. {6,-2+2j-2,-2-2j}

B. {6,-2-2j,2,-2+2j}

C. {6,-2-2j,-2,-2+2j}

D. {6,-2+2j,-2,-2-2j}

20. If W4100=Wx200, then what is the value of x?

A. 2

B. 4

C. 8

D. 16

21. The frequency transformation in the digital domain involves replacing the variable z-1 by a rational function g(z-1).

A. True

B. False

22. The mapping z-1 → g(z-1) must map inside the unit circle in the z-plane into __________

A. Outside the unit circle

B. On the unit circle

C. Inside the unit circle

D. None of the mentioned

23. The unit circle must be mapped outside the unit circle.

A. True

B. False

24. The mapping z-1 → g(z-1) must be __________

A. Low pass

B. High pass

C. Bandpass

D. All-pass

25. What should be the value of |ak| to ensure that a stable filter is transformed into another stable filter?

A. < 1

B. =1

C. > 1

D. 0

26. Which of the following methods are inappropriate to design high pass and many bandpass filters?

A. Impulse invariance

B. Mapping of derivatives

C. Impulse invariance & Mapping of derivatives

D. None of the mentioned

27. The impulse invariance method and mapping of derivatives are inappropriate to use in the designing of high pass and bandpass filters due to the aliasing problems.

A. True

B. False

28. We can employ the analog frequency transformation followed by conversion of the result into the digital domain by use of impulse invariance and mapping the derivatives.

A. True

B. False

29. It is better to perform the mapping from an analog low pass filter into a digital low pass filter by either of these mappings and then perform the frequency transformation in the digital domain.

A. True

B. False

30. In which of the following transformations, it doesn’t matter whether the frequency transformation is performed in the analog domain or in the frequency domain?

A. Impulse invariance

B. Mapping of derivatives

C. Bilinear transformation

D. None of the mentioned