(Solved): (17 pts) An LTI system with impulse response \( h[n] \) is formed by cascading two LTI systems with ...

(17 pts) An LTI system with impulse response \( h[n] \) is formed by cascading two LTI systems with impulse responses \( h_{1}[n] \) and \( h_{2}[n] \) as shown below. You are told that \( h_{1}[n]=u[n] \) and that \( h_{2}[n]=\delta[n]-\delta[n-1] \). We know that \( h_{1}[n] \) is an accumulator system (and can be viewed as a discrete-time approximation of a continuoustime integrator system), while \( h_{2}[n] \) is a finite difference system (and can be viewed as a discrete-time approximation of a continuous-time differentiator system). (a) Is \( h_{1}[n] \) a BIBO stable system? Explain. (b) Is \( h_{2}[n] \) a BIBO stable system? Explain. (c) Calculate a closed-form expression for \( h[n] \) that is valid for all \( n \in \mathbb{Z} \). Your final answer should not have any unresolved summations. (d) Given your answer from (c), what type of system is \( h[n] \) ? (In other words, how would you describe the effects of the system \( h[n] \) on the input signal?)