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

1. The N^{th} root of unity W_{N} is given as _____________

a) e^{j2πN}

b) e^{-j2πN}

c) e^{-j2π/N}

d) e^{j2π/N}

2. Which of the following is true?

a) W∗N=1NWN−1

b) WN−1=1NWN∗

c) WN−1=WN∗

d) None of the mentioned

3. 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}

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

a) X(k)=Nc_{k}

b) X(k)=c_{k}/N

c) X(k)=N/c_{k}

d) None of the mentioned

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

a) N^{2} complex multiplications and N(N-1) complex additions

b) N^{2} complex additions and N(N-1) complex multiplications

c) N^{2} complex multiplications and N(N+1) complex additions

d) N^{2} complex additions and N(N+1) complex multiplications

6. If W_{4}^{100}=W_{x}^{200}, then what is the value of x?

a) 2

b) 4

c) 8

d) 16

7. Which of the following operation is performed by the blocks given 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

8. 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

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. 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