Frequency Response

#Math

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

• The fourier transform of the impulse function

$\displaystyle \lvert Y(j\omega)\rvert=\lvert H(j\omega)\rvert\lvert X(j\omega)\rvert$

• Scales the amplitude of response

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

• Shifts the phase response

$\displaystyle y(t)=\lvert H(j{\omega}{0})\rvert e^{j(\omega t+\angle H(j{\omega}{0}))}$

• For $\displaystyle x(t)=e^{j{\omega}_{0}t}$