(a) Let h[n] and g[n] be the impulse responses of two stable discrete-time LTI systems t...

(a) Let h[n] and g[n] be the impulse responses of two stable discrete-time LTI systems that are inverses of each other. What is the relationship between the frequency responses of these two systems?

(b) Consider causal LTI systems described by the following difference equations. In 'each case, determine the impulse responsible inverse system and the difference equation that characterizes the inverse.

What is the inverse of this system? Show that the inverse is not causal. Find an-other causal LTI system that is an "inverse with delay" of the system described by eq. (P5.36-1). Specifically, find a causal LTI system such that the output w[n] in Figure P5.36 equals x[n - 1].