(Solved): Q1. i) State Associative property of Convolution. ii) Prove the above property for the sequence \[ ...

Q1. i) State Associative property of Convolution. ii) Prove the above property for the sequence \[ x(n)=\left\{\begin{array}{c} 2,-1,3 \\ \uparrow \end{array}\right\} ; h_{1}(n)=\{3,2,1\} ; h_{2}(n)=\left\{\begin{array}{c} 1,-2,1 \\ \uparrow \end{array}\right\} \] Q2. Apply the Commutative property of Convolution to find the response of a LTI system for the following two inputs. \[ x(t)=\left\{\begin{array}{l} 5 ;-1 \leq t \leq 1 \\ 0 ; \text { otherwise } \end{array} \& h(t)=\left\{\begin{array}{l} t ; 0 \leq t \leq 2 \\ 0 ; \text { otherwise } \end{array}\right.\right. \] Q3. i) Obtain the Transfer function of the given LTI system whose pole-zero plot is shown in figure 1. figure 1. ii) Is the above system stable?