Problem

Figure P8.16-1 shows a six-point discrete-time sequence x[n]. Assume that x[n] = 0 outsi...

Figure P8.16-1 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. Note that the sample shown for b in the figure is not necessarily to scale. Let X(e^j^ω) be the DTFT of x[n] and X₁[k] be samples of X(e^j^ω) every π/2; i.e.,

The four-point sequence x₁[n] that results from taking the four-point inverse DFT of X₁[k] is shown in Figure P8.16-2. Based on this figure, can you determine b uniquely? If so, give the value for b.