In Figure P3.43, h[n] is the impulse response of the LTI system within the inner box. The input to system h[n] is v[n], and the output is w[n]. The z-transform of h[n], H (z), exists in the following ROC:
(a) Can the LTI system with impulse response h[n] be bounded input, bounded output stable? If so, determine inequality constraints on rmin and rmax such that it is stable. If not, briefly explain why.
(b) Is the overall system (in the large box, with input x[n] and output y[n]) LTI? If so, find its impulse response g[n]. If not, briefly explain why
c) Can the overall system be BIBO stable? If so, determine inequality constraints relating α, rmin, and rmax such that it is stable. If not, briefly explain why
