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Which of the following statement(s) is/are true?
If an LTI system is causal, it is stable.
A discrete time LTI system is causal if and only if its response to a step input 
is 0 for 
.
If a discrete time 
system has an impulse response 
of finite duration the system is stable.
If the impulse response 
for all 
, then the LTI system is stable.
(a) for a causal LTI system, h[n] = 0 ∀ n < 0 & for stability
∴ Causal LTI system may or may not be stable.
(b) for causal LTI system, h[n] = 0 ∀ n < 0
Step response, s[n] = u[n] * h[n]
∴ both u[n] & h[n] = 0 ∀ n < 0
∴ S[n] = 0 ∀ n < 0
(c) if h[n] has finite duration, then system may or may not be stable
Has finite duration but h[n] is not absolutely summable ∴ system is unstable.
(d) if 0 < |h[n]| < 1 then system may be unstable because if signal has infinite duration then h[n] is not absolutely summable.