4< Res <-1: Not Causal. Not Stable 1< es)<2: Not Causal. Stable 2<e{s} Causal. Not Stable Problem 2 Draw a direct-form representation for the causal lti system with system function H Note that the system function can be represented as follow H(s) (s+3)(s+4) s2+7s+12 w(s)X(s) Thus, we can see the system H(s)as a cascade of two systems, i. e, Z(s)=wo which accounts for the zeros and P(s)=yio which accounts for the poles First, let's draw a block diagram representation of the system P(s). Since the system is of second order, we would like to represent the system using only two integrators in cascade w(t) w(t) w(t) (t)−4 < √e{s} < −1 : Not Causal. Not Stable −1 < √e{s} < 2 : Not Causal. Stable 2 < √e{s} : Causal. Not Stable Problem 2 Draw a direct-form representation for the causal LTI system with system function s(s + 1) H(s) = . (s + 3)(s + 4) Note that the system function can be represented as follows: H(s) = s(s + 1) (s + 3)(s + 4) s2 + s = s2 + 7s + 12 = Y (s) W(s) W(s) X(s) = � �� � s2 + s 1 s2 + 7s + 12 . Y (s) � �� � W(s) W(s) X(s) Y (s) Thus, we can see the system H(s) as a cascade of two systems, i.e., Z(s) = W(s) which accounts W(s) for the zeros and P(s) = X(s) which accounts for the poles. First, let’s draw a block diagram representation of the system P(s). Since the system is of second order, we would like to represent the system using only two integrators in cascade. x(t) +− w¨(t) 1 s 1 s w˙ (t) 7 w(t) 12 + 5