The discrete-time **impulse response** is the output of a discrete-time [[system]] when the input signal is a [[discrete-time unit impulse]]: $h(n)=S(\delta(n))$ Since any [[discrete-time signal]] can be represented as a [[sum of impulses]], the impulse response can be used to compute the output of a [[discrete-time LTI system]] to any [[discrete-time signal]] (see [[response to a sum of impulses]]).