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

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)

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**

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

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}

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}*=1NW−1N**b) W _{N}^{-1}=1NWN∗**

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 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