1. Consider the two-port communication system shown in Fig. 1. (LPF) If an input autocorrelation Rxx (I) is given by Bxx (T) = BeITI, B'>0, 320, all I's 1.1. Determine the output autocorrelation using the Wiener- Khintchive theorem 1.2. Find the output noise, by XINPOT Y: OUTPUT Rxx (T) "Ryy (t) FIG. 1. 5y 2 =x 8 HINT: Ryy (t) = 3" { Syy(w)} = (syy (w) e+jww, Syy (w) = | H(w)|= 3x(w) ff(2)dz = lim [ {(w/dw + for fre)da = jam Res f (zi) R if(z)dz State-space equation of given below D linear autonomous system cre 1-5/3 x(+)=-1/3 4/30 0 dt 13 x(+) 0 -2 a) find the et state transition matrix of system by the Lapalace transform b) find the et state transition matrix of system with the Cayley-Hamilton Theorem c) find the et state transition matrix of system. using eigenvectors 1- A- B = 9 1 00 20-601 9 00 x = Ax+ B4 0 0 ol -0.4905 y= Cx 0 0 c = [0 010] Applying the state space theories to determine the transition matrix of this system. Show steps. m debil.