Impulse response ($h=\mathcal F^{-1}[H]$)

The time-domain function whose Fourier transform is a filter's frequency response.

A filter's impulse response, $h=\mathcal F^{-1}[H]$ , is the time-domain function such that filtering by convolution, $y=h*x$ , matches multiplying by the frequency response $H(\omega)$ in the frequency domain. It is, literally, what the filter's output looks like when its input is a single Dirac delta impulse.

Examples

A filter whose impulse response is a narrow positive bump acts as a smoothing (low-pass) filter.