In Figure, 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 region of convergence:

0 ?min max

(a) Can the LTI system with impulse response h[n] BIBO stable? If so, determine inequality constraints on r_min and r_max 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 a, r_min, and r_max such that it is stable. If not, briefly explain why.

Transcribed Image Text:

h[n] LTI * [n] * [n] v[n] y[n]