Define \(\left\{x_{I}(n), k=1,-1,1ight\}\) and \(\left\{x_{Q}(n), k=1,1,-1ight\}\). (a) Compute the discrete correlations: \(\boldsymbol{R}_{x_{I}}, \boldsymbol{R}_{x_{Q}}, \boldsymbol{R}_{x_{I}}, \boldsymbol{R}_{x_{Q}}\), and \(\mathfrak{R}_{x_{Q} x_{I}}\). (b) A certain radar transmits the signal \(s(t)=x_{I}(t) \cos \left(2 \pi f_{0} tight)-x_{Q}(t) \sin \left(2 \pi f_{0} tight)\). Assume that the autocorrelation \(s(t)\) is equal to \(y(t)=y_{I}(t) \cos \left(2 \pi f_{0} tight)-y_{Q}(t) \sin \left(2 \pi f_{0} tight)\). Compute and sketch \(y_{I}(t)\) and \(y_{Q}(t)\).