# Frequency Domain Sampling

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 Nth rot of unity WN is given as ______________
a) ej2πN
b) e-j2πN
c) e-j2π/N
d) ej2π/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) WN*=1NW−1N
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}

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