Question

Consider the LTI system: Express the system impulse response as a function of the impulse responses of the subsystems. 2. An LTI system has the impulse response h(t)=e −3t μ(t−1) (a) Determine whether this system is causal. (b) Determine whether this system is stable.

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Answer 1

The impulse response of the given LTI system is e^(-3t)u(t-1). The system is causal because the impulse response is zero for t less than one. The system is stable because the impulse response is absolutely integrable.

Step-by-step explanation:

For an LTI system, the impulse response of the system can be expressed as a function of the impulse responses of the subsystems. In this case, the impulse response of the system is given by h(t) = e^(-3t)u(t-1), where u(t) is the unit step function.

(a) To determine whether this system is causal, we need to check if h(t) is zero for t less than zero. From the expression of h(t), it is clear that h(t) is zero for t less than one. Therefore, the system is causal.

(b) To determine whether this system is stable, we need to check if the impulse response is absolutely integrable. In this case, the impulse response is e(-3t)u(t-1), which is absolutely integrable. Hence, the system is stable.