Question

Given the real signal: x [n] = [1, -2,0,1], indicate the correct alternative:
a) The DFT of the signal with 6 points is [0, -1 + 1.7321j, 3 + 1.7321j, 2.3-1.7321j, -1-1.7321j]
b) The DFT of the signal with 5 points is:
[0,0,0, j, -j]
c) The DFT of the signal with 7 points does not allow the original signal to be recovered.
d) The DFT of the signal with 4 points is: x [n] = [-2, -1 + 1j, -4, -1-1j]

Answer 1

Option (C) is incorrect because any DFT with N>=4 can be used to recover x[n] from it's DFT X[K].

Option (D) is incorrect because X[0]=1-2+0+1=0,but given it is -2.

Option (B) is incorrect because as x[n] is real signal , X[K] =X*[N-K]=X*[5-K],but X[1]=0 and X*[5-1]=X*[4]=(-j)*=j ,which is not equal to X[1]=0.

Option (A) is incorrect, because it has only 5 points,it can't be the 6 point DFT of x[n].

Option (A) can be modified by including the X[3]=2,it can be made correct.