# Frequency Domain Sampling MCQ’s

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

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}

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

3. A finite duration sequence of length L is given as x(n)=1 for 0≤n≤L-1 = 0 otherwise, then what is the N point DFT of this sequence for N=L?

a) X(k) = L for k=0, 1, 2….L-1

b)

```
X(k) = L for k=0
=0 for k=1,2....L-1
```

c)

X(k) = L for k=0 =1 for k=1,2....L-1

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}

4. The N^{th} rot of unity W_{N} is given as ______________

a) e^{j2πN}

b) e^{-j2πN}

c) e^{-j2π/N}

d) e^{j2π/N}

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

1. If x(n) is a finite duration sequence of length L, then the discrete Fourier transform X(k) of x(n) is given as ____________

a) ∑N−1n=0x(n)e−j2πkn/N(L<N)(k=0,1,2…N-1)

b) ∑N−1n=0x(n)ej2πkn/N(L<N)(k=0,1,2…N-1)

c) ∑N−1n=0x(n)ej2πkn/N(L>N)(k=0,1,2…N-1)

d) ∑N−1n=0x(n)e−j2πkn/N(L>N)(k=0,1,2…N-1)

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

a) 2

b) 4

c) 8

d) 16

6. Which of the following is true?

a) W_{N}*=1NW−1N

b) W_{N}^{-1}=1NWN∗

c) W_{N}^{-1}=W_{N}*

d) None of the mentioned

2. If X(k) discrete Fourier transform of x(n), then the inverse discrete Fourier transform of X(k) is?

a) 1N∑N−1k=0X(k)e−j2πkn/N

b) ∑N−1k=0X(k)e−j2πkn/N

c) ∑N−1k=0X(k)ej2πkn/N

d) 1N∑N−1k=0X(k)ej2πkn/N

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