The inverse of an LTI system H(s) is defined as a system that, when cascaded with H(s),...

The inverse of an LTI system H(s) is defined as a system that, when cascaded with H(s), results in an overall transfer function of unity or, equivalently, an overall impulse response that is an impulse.

(a) If denotes the transfer function of an inverse system for H(s), determine the general algebraic relationship between H(s) and .

(b) Shown in Figure P9.48 is the pole-zero plot for a stable, causal system H(s). Determine the pole-zero plot for the associated inverse system.