Question

What is the impulse response of the LTI system?

1) h(t) = e⁽⁻ᵗ⁾u(t)
2) h(t) = e⁽⁻ᵗ⁾
3) h(t) = u(t)
4) h(t) = 1

Answer 1

The correct impulse response of a causal LTI system from the provided options is h(t) = e^(-t)u(t), which includes the unit step function to ensure causality.

Step-by-step explanation:

The impulse response of an LTI (Linear Time-Invariant) system characterizes the system's response to an impulse function. Among the given options:

1. h(t) = e^(-t)u(t) where u(t) is the unit step function, represents the impulse response of an LTI system that starts at t=0. This function includes the effect of the unit step function u(t) to ensure causality.
2. h(t) = e^(-t) represents a signal that would start at t = -∞, which is not physically realizable for causal systems.
3. h(t) = u(t) represents the impulse response of an ideal integrator.
4. h(t) = 1 is a constant function and does not represent the impulse response of an LTI system.

Thus, the correct impulse response for a causal LTI system from the options given is h(t) = e^(-t)u(t).