1. 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

2. 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

3. 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

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

A. e^{j2πN}

B. e^{-j2πN}

C. e^{-j2π/N}

D. e^{j2π/N}

5. 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

6. 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

7. 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}

8. 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

9. 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}

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

A. 2

B. 4

C. 8

D. 16

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

A. True

B. False

12. 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

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

A. True

B. False

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

A. Low pass

B. High pass

C. Bandpass

D. All-pass

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. Which of the following is the first method proposed for the design of FIR filters?

A. Chebyshev approximation

B. Frequency sampling method

C. Windowing technique

D. None of the mentioned

22. The lack of precise control of cutoff frequencies is a disadvantage of which of the following designs?

A. Window design

B. Chebyshev approximation

C. Frequency sampling

D. None of the mentioned

23. The values of cutoff frequencies, in general, depend on which of the following?

A. Type of the window

B. Length of the window

C. Type & Length of the window

D. None of the mentioned

24. In the frequency sampling method, the transition band is a multiple of which the following?

A. π/M

B. 2π/M

C. π/2M

D. 2πM

25. The frequency sampling design method is attractive when the FIR filter is realized in the frequency domain by means of the DFT.

A. True

B. False

26. Which of the following values can a frequency response take in the frequency sampling technique?

A. Zero

B. One

C. Zero or One

D. None of the mentioned

27. Which of the following technique is more preferable for the design of a linear phase FIR filter?

A. Window design

B. Chebyshev approximation

C. Frequency sampling

D. None of the mentioned

28. By optimal filter design, the maximum sidelobe level is minimized.

A. True

B. False

29. Which of the following is the correct expression for transition band Δf?

A. (ωp– ωs)/2π

B. (ωp+ωs)/2π

C. (ωp.ωs)/2π

D. (ωs– ωp)/2π

30. If the resulting δ exceeds the specified δ2, then the length can be increased until we obtain a side lobe level that meets the specification.

A. True

B. False