Figure shows a six-point discrete-time sequence x[n]. Assume that x[n] = 0 outside the interval shown. The value of x[4] is not known and is represented as b, that the sample shown for b in the figure is not necessarily to scale, Let X(e^j?) be the DTFT of x[n] and X₁[k] be samples of X(e^j?) every ?/2; i.e.,

X1[k] = X(e^j?)|_{? =(?/2)k}, ? ? ? ? ? ??0 ? k ? 3.

The four-point sequence x₁[n] that results from taking the four-point inverse DFT of X₁[k] is shown in Figure. Based on this figure, can you determine b uniquely? If so, give the value for b.

*[n] x{n] 2 x[n] 2 3 4 1 2.