Figure P10.18 shows the magnitude |V [k]| of the 128-point DFT V [k] for a signal v[n]....

Figure P10.18 shows the magnitude |V [k]| of the 128-point DFT V [k] for a signal v[n]. The signal v[n] was obtained by multiplying x[n] by a 128-point rectangular window w[n]; i.e., v[n] = x[n]w[n]. Note that Figure P10.18 shows |V [k]| only for the interval 0 ≤ k ≤ 64. Which of the following signals could be x[n]? That is, which are consistent with the information shown in the figure?

x ₁[n] = cos(πn/4) + cos(0.26πn),

x ₂[n] = cos(πn/4) + (1/3) sin(πn/8),

x ₃[n] = cos(πn/4) + (1/3) cos(πn/8),

x ₄[n] = cos(πn/8) + (1/3) cos(πn/16),

x ₅[n] = (1/3) cos(πn/4) + cos(πn/8),

x ₆[n] = cos(πn/4) + (1/3) cos(πn/8 + π/3).