# Frequency Response

$H(jw)$ is called the frequency response, where $H(s)$ is simply the Transfer Function.

$H(jω)=∣H(jω)∣e_{j∠_{H(jω)}}$

Theorem 1

If $S:f→y$ is a LTI then for any $s∈C$ $e_{st}→H(s)e_{st}$

- Taken from LTI System page

Theorem 2

If $S:f→y$ is a LTI then

$sin(ωt)→∣H(jω)∣sin(ωt+∠_{H(jω)})$

Theorem 3

If $S$ is a stable LTI with transfer function $H(s)$, then as $t→∞$

$sin(ωt)u(t)→∣H(jω)∣sin(ωt+∠_{H(jω)})$