Question

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}

The question was asked in an online quiz.

My doubt stems from Frequency Domain Sampling DFT in division Discrete Fourier Transform – Properties and Applications of Digital Signal Processing

Answer 1

The correct answer is (d) {6,-2+2j,-2,-2-2j}

For explanation: Given x(n)={0,1,2,3}

We know that the 4-point DFT of the above given sequence is given by the expression

X(k)=\(\sum_{n=0}^{N-1}x(n)e^{-j2πkn/N}\)

In this case N=4

=>X(0)=6,X(1)=-2+2j,X(2)=-2,X(3)=-2-2j.