Frequency Response

$H(j\omega )=\mathcal{F}[h(t)]$

• The fourier transform of the impulse function

$|Y(j\omega )|=|H(j\omega )||X(j\omega )|$

• Scales the amplitude of response

$\angle Y(j\omega )=\angle H(j\omega )+\angle X(j\omega )$

• Shifts the phase response

$y(t)=|H(j{\omega }_0)|e^{j(\omega t+\angle H(j{\omega }_0))}$

• For $x(t)=e^{j{\omega }_{0}t}$