Determine whether each of the following statements concerning LTI systems is true or fal...

Determine whether each of the following statements concerning LTI systems is true or false. Justify your answers.

(a) If h(t) is the impulse response of an LTI system and h(t) is periodic and nonzero, the system is unstable.

(b) The inverse of a causal LTI system is always causal.

(c) If K for each n, where K is a given number, then the LTI system with h[n] as its impulse response is stable.

(d) If a discrete-time LTI system has an impulse response h[n] of finite duration, the system is stable.

(e) If an LTI system is causal, it is stable.

(f) The cascade of a noncausal LTI system with a causal one is necessarily noncausal.

(g) A continuous-time LTI system is stable if and only if its step response s(t) is absolutely integrable--that is, if and only if

(h) A discrete-time LTI system is causal if and only if its step response s[n] is zero for n < 0.