Consider the cascade of an LTI system with its inverse system shown in Figure P5.29....

Consider the cascade of an LTI system with its inverse system shown in Figure P5.29.

The impulse response of the first system is h[n] = δ[n] + 2δ[n − 1].

(a) Determine the impulse response h_i [n] of a stable inverse system for h[n]. Is the inverse system causal?

(b) Now consider the more general case where h[n] = δ[n] + αδ[n − 1]. Under what conditions on α will there exist an inverse system that is both stable and causal?