Arrange the FFT of x[n] = {0, 1,2,3}...

 

FFT of x[n] = {0, 1, 2, 3}

We compute the 4-point DFT using:

X[k] = Σ x[n] e^-j(2π/4)kn, for k = 0,1,2,3

Let W = e^-jπ/2 = -j

Step-by-step Calculation

1. X[0]
X[0] = 0 + 1 + 2 + 3 = 6

2. X[1]
X[1] = 1(-j) + 2(-1) + 3(j)
= -j - 2 + 3j = -2 + 2j

3. X[2]
X[2] = 1(-1) + 2(1) + 3(-1)
= -1 + 2 - 3 = -2

4. X[3]
X[3] = 1(j) + 2(-1) + 3(-j)
= j - 2 - 3j = -2 - 2j

Final Answer: option 3

X[k] = {6, -2 + 2j, -2, -2 - 2j}