Digital Signal Processing Questions and Answers – Frequency Domain Sampling DFT

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:

View Answer

Answer: a
Explanation: If x(n) is a finite duration sequence of length L, then the Fourier transform of x(n) is given as

If we sample X(ω) at equally spaced frequencies ω=2πk/N, k=0,1,2…N-1 where N>L, the resultant samples are

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

View Answer

Answer: d
Explanation: If X(k) discrete Fourier transform of x(n), then the inverse discrete Fourier transform of X(k) is given as

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
View Answer

Answer: b
Explanation: The Fourier transform of this sequence is

If N=L, then X(k)= L for k=0
=0 for k=1,2….L-1

4. The Nth rot of unity W_N is given as:
a) e^j2πN
b) e ^-j2πN
c) e^-j2π/N
d) e^j2π/N
View Answer

Answer: c
Explanation: We know that the Discrete Fourier transform of a signal x(n) is given as
Thus we get Nth rot of unity WN= e^-j2π/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
View Answer

Answer: a
Explanation: The formula for calculating N point DFT is given as

From the formula given at every step of computing we are performing N complex multiplications and N-1 complex additions. So, in a total to perform N-point DFT we perform N² complex multiplications and N(N-1) complex additions.

6. Which of the following is true?
d) None of the mentioned
View Answer

Answer: b
Explanation: If XN represents the N point DFT of the sequence xN in the matrix form, then we know that

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 Answer

Answer: c
Explanation: The first step is to determine the matrix W4. By exploiting the periodicity property of W4 and the symmetry property
W_N^k+N/2= -W_N^k
The matrix W₄ may be expressed as

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
View Answer

Answer: a
Explanation: The Fourier series coefficients are given by the expression

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}
View Answer

Answer: d
Answer: Given x(n)={0,1,2,3}
We know that the 4-point DFT of the above given sequence is given by the expression

In this case N=4
=>X(0)=6,X(1)=-2+2j,X(2)=-2,X(3)=-2-2j.

10. If W₄¹⁰⁰=W_x²⁰⁰, then what is the value of x?
a) 2
b) 4
c) 8
d) 16
View Answer

Sanfoundry Global Education & Learning Series – Digital Signal Processing.

To practice all areas of Digital Signal Processing, here is complete set of 1000+ Multiple Choice Questions and Answers.