e(t), E(s) LE*(s),E(z) Y(z) G (s) = G,(s)GH(s) c(t), C(s) D(z) To =G,(s)(1-0STOVS For the system above: D(z)=1+ 0.5z1, GP(s)=5/(s+4), GHO(S)= (1-e*T0)/s, To=1/2 26. As in the class notes, for the system above define Gc(s) = G'(s) (1-esTO). Then, G'(s)= a) Tos?(s+4) b) s(s+4) 4sTo c) s(s+5) d) none above 27. As in the class notes, for the system above, G'(z)= 5z(1-e-4To) a)· 4(z-1)(z-e-4To) 5T, (z-e-To/5) b) 4z(1-e-To/5) 5(z-1)(1-e-4To) 4(z+1)(z-e-4To) d) none above 28. In the system above, the open-loop pulse transfer function (excluding ROC) is G(z)=C(z)/E(z)= 57, (2z-1)(z-e-4TO) a) 8(z+1)(1-e-4To) 5(2z+1)(1-e-4To) b) 8z(z-e-4To) 5(z-1)(2z+1) c) 4z(z-e-STo) d) none above 29. In the system above, the open-loop dc gain GOL(s)=C(s)/E(s) of the system is a) 1.9 b) 2.6 c) 5.2 d) none above 30. In the system above, the open-loop gain GOL(s)=C(s)/E(s) of the system at 1 Hz is a) -2.3 b) -0.48 c) 0.31 d) none above

Prove the Parseval's Theorem: N-1 N-1 1 EX k]X*[k] n=0 k=0 Hint: 1. Use different variables for difference summations. 2. Change the ordering of summa- tions. 3. Use the important geometric sum on the first page.

compute and sketch the convolution between following pair of signals: h[n] = (1/2)^n u[n-4], x[n] = 4^n u[2-n]

For the below system, find the rang of ? that make the below system stable