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Which of the following statement(s) is/are true? (A) If an LTI system is causal, it is stable (B) A discrete time LTI system is causal if and only if its response to a step input u[n] is 0 for n < 0 (C) If a discrete time LTI system has an impulse response h[n] of finite duration the system is stable (D) If the impulse response 0 < |h[n]| < 1 for all n, then the LTI system is stable.

1. (A)
2. (B)
3. (C)
4. (D)

Correct answer: (C)

Solution

A discrete time LTI system with a finite duration impulse response means that the system's output will eventually settle to a steady state, ensuring that it does not produce unbounded outputs for bounded inputs, which is the definition of stability.

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