$p(n)=x(n)cos⁡(n π/2) \\ p(n)=\bigg(\frac{e^{j nπ/2}+e^{-j nπ/2}}{2}\bigg) x(n) \\ p(n)= \frac{1}{2}\bigg[e^{j nπ/2} x(n)+e^{-j nπ/2} x(n)\bigg] \\ By \ Frequency \ Shift \ Property, \\ Q(k)=\frac{1}{2}[X(k-1)+X(k+1)] \\ Q(k)=\frac{1}{2} \bigg(\begin {bmatrix} \ 4 \\ 1 \\ 2 \\ 3\end{bmatrix}+ \begin {bmatrix} \ 2 \\ 3 \\ 4 \\ 1\end{bmatrix}\bigg) \\ Q(k)= \begin{bmatrix} \ …