Figure P8.35-1 illustrates a six-point discrete-time sequence x[n]. Assume that x[n] is...

Figure P8.35-1 illustrates a six-point discrete-time sequence x[n]. Assume that x[n] is zero outside the interval shown.

The value of x[4] is not known and is represented as b. The sample in the figure is not shown to scale. Let X(e^jω) be the DTFT of x[n] and X₁[k] be samples of X(e^jω) at ω_k = 2πk/4, i.e.,

The four-point sequence x₁[n] that results from taking the four-point inverse DFT of X₁[k] is shown in Figure P8.35-2. Based on the figure can you determine b uniquely? If so, give the value of b.