Frequency domain ($\hat{f}(\omega )$)

A time-dependent response can be represented by its Fourier transform in angular frequency. With $\hat{f}(\omega )=\int f(t)e^{i\omega t}dt$, a time derivative transforms to $-i\omega \hat{f}$ 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 $e^{-i\omega t}$.