Question

Determine whether or not each of the following LTI systems given by either the impulse response h(t) or the input-output relation is (i) causal and/or (ii) BIBO stable.

h(t) = e⁻∣ᵗ∣

Answer 1

An LTI system with impulse response h(t) = e^(-t) is not causal but is BIBO stable.

Step-by-step explanation:

An LTI (Linear Time-Invariant) system is said to be causal if its output only depends on past and present values of the input, and not future values. Causality can be determined by looking at the impulse response:

If the impulse response h(t) is 0 for t < 0, then the system is causal. In this case, the impulse response h(t) = e^(-t) is non-zero for t < 0, which means the system is not causal.

A system is said to be BIBO (Bounded-Input Bounded-Output) stable if every bounded input produces a bounded output. BIBO stability can be determined by looking at the impulse response:

If the impulse response h(t) is absolutely integrable, then the system is BIBO stable. In this case, the impulse response h(t) = e^(-t) is absolutely integrable, which means the system is BIBO stable.