# Sampling Rate Conversion

This set of tough Digital Signal Processing Questions & Answers focuses on “Sampling Rate Conversion by a Rational Factor I/D”.

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 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 N^{th} root of unity W_{N} 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) 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. Which of the following is true?

a) W∗N=1NWN−1**b) WN−1=1NWN∗**

c) WN−1=WN∗

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}

View AnswerAnswer: c

Explanation: The first step is to determine the matrix W_{4}. By exploiting the periodicity property of W_{4} and the symmetry property

Wk+N/2N=−WNk

The matrix W_{4} may be expressed as

W_{4}=⎡⎣⎢⎢⎢⎢W04W04W04W44W04W04W24W64W04W24W04W64W14W34W34W94⎤⎦⎥⎥⎥⎥=⎡⎣⎢⎢⎢⎢W04W04W04W04W04W04W24W24W04W24W04W24W14W34W34W14⎤⎦⎥⎥⎥⎥

=⎡⎣⎢⎢⎢11111−j−1j1−11−11j−1−j⎤⎦⎥⎥⎥

8. 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

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

a) 2

b) 4**c) 8**

d) 16