impulse response

The impulse response h(t) is how an LTI system reacts when you hit it with a single, infinitely-short, infinitely-tall spike — the Dirac delta δ(t). The vivid way to grasp it: clap once, sharply, in an empty cathedral. The slowly-fading reverberation you hear afterwards IS the room's impulse response. That one clap reveals everything the room will do to any sound.

Its power is that h(t) is a complete fingerprint of the system. Because any input can be sliced into a dense train of tiny scaled-and-delayed impulses, and because the system is linear and time-invariant, the total output is just the sum (the convolution) of a delayed-and-scaled copy of h(t) for each input slice. This is why audio reverb plugins literally store the impulse response of famous concert halls — convolving your dry track with that h(t) places your music inside the hall.