Impulse Response

In Digital Signal Processing, Impulse Response is the output of a system when it is subjected to an Impulse.

For example, the impulse response of a reverb filter would continuously fade the volume from the impulse over time. An echo filter would periodically repeat the impulse, while fading the volume over time. A gain filter would have no temporal effect like the aforementioned.

$h[n]$ is used to denote the impulse response of a system where

$$h[n]=T\{\delta [n]\}$$

Impulse response is important in DSP because if a system in a Linear Time-Invariant System, then knowing $h[n]$ means you know everything about the system, where $T$ is the system.

$$T\{x[n]\}=x[n]\ast h[n]$$