Let us consider the case where a vector \(\{\mathbf{X}(n)\}\) represents an \(M \times 1\) WSS process, and that

\[Y_{i}(n)=W_{i}(n) X_{i}(n)\]

for \(i=0,1, \ldots, M-1\). Show that \(\{\mathbf{Y}(n)\}\) is WSS if and only if \(W_{i}(n)=\kappa_{i} \mathrm{e}^{\mathrm{j} \phi_{i} n}\). This result indicates that the only time dependency between \(Y_{i}(n)\) and \(X_{i}(n)\) is at the exponent, where \(\kappa_{\mathrm{i}}\) is a possibly complex constant and \(\phi_{i}\) is a real constant.