Frequency domain (source code)

= Frequency domain
{title2=$\widehat f(\omega)$}

A time-dependent response can be represented by its <Fourier transform> in <angular frequency>. With $\widehat f(\omega)=\int f(t)e^{i\omega t}dt$, a <time derivative> transforms to $-i\omega\widehat f$ when boundary terms vanish. A time-translation-invariant response convolution becomes multiplication by a <frequency>-dependent response coefficient. This is why a dispersive <electrical conductivity> is naturally specified in the frequency domain. The inverse-transform modes use $e^{-i\omega t}$.