Many audio effects with delay can be measured using a process called an impulse response (IR). For this measurement, the output of an audio effect is recorded for an impulse input signal. Here is a demonstration of the process using a digital audio workstation (DAW) application.
This input signal has an amplitude of zero for all samples except for the first sample, which has an amplitude of 1. Therefore, an IR is a measurement of what happens to a single sample when it goes through the system by itself.
An intuitive way to understand an IR is to consider its use with echo effects. These types of systems will delay the impulse to a different sample at a later point in time. An effect with more than one delayed repetition (i.e. feed-back echo or multi-tap echo) will have more than one delay impulse appearing in the IR.
Furthermore, a system’s IR is also used to represent, describe, and model the system itself. In Matlab, a system is represented as an array of samples from the IR. Each element in the array corresponds to the gain coefficient for that number of samples of delay.
Audio engineers save IRs as .wav files even though it represents a system and not a signal. These .wav files can be loaded into a convolution plug-in (e.g. Altiverb, Waves IR-1, Logic Space Designer, etc.) to model the measured system. Additionally, the IR can be used with the Matlab convolution function.