Analyze LTI systems in the s-domain. Definition

$$ X(s) = \mathcal{L}\{x(t)\} = \int_0^{\infty} x(t) e^{-st} dt $$

Where $s = \sigma + j\omega$ is a complex frequency. Common Transforms $x(t)$ $X(s)$ ROC $\delta(t)$ $1$ All $s$ $u(t)$ $\frac{1}{s}$ $\text{Re}(s) > 0$ $e^{-at}u(t)$ $\frac{1}{s+a}$ $\text{Re}(s) > -a$ …

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