It is known that the output of a distortionless linear system is given by y(t)-Ax(t-t), where A is the gain of the system, t is the time delay, x(t) is the input. It is often convenient to evaluate the performance of a linear system by comparing the system output with an amplitude-scaled and time-delayed version of the input. The mean square error is then (A, T) = [y (t)- Ax (t - T)] The values of A and t that minimize this expression, denoted Am and tm, respectively, are defined as the system gain and system delay. Show that, with these definitions, Rxy (Tm) Am = a. The system gain is R, (0) 2 (Am, Tm) R,(0) - = Ray (Tm) R, (0) b. And the resulting system mean-squared error is c. Also show that the signal power at the s R, (Tm) SD = A R (0) d. System output is R, (0) SD R, (Tm) = e. The output SNR ratio is No R. (0) R, (0)-R2, (Tm); Np is the mean-square error