(Solved): The figure below shows a connection of two causal discrete-time LTI systems. a) Determine the over ...

The figure below shows a connection of two causal discrete-time LTI systems. a) Determine the overall system function \( H(z) \), assuming the impulse responses of the systems are \[ \begin{array}{l} h_{1}[n]=0.3^{n} u[n] \\ h_{2}[n]=(-0.5)^{n} u[n] \end{array} \] b) Assuming the overall system function is \( H(z)=\frac{2+3 z^{-1}-z^{-2}}{1-0.4 z^{-1}} \) and \( h_{1}[n]=0.4^{n} u[n] \), find and sketch the impulse response \( h_{2}[n] \).