= Impulse response
{title2=$Lu=\delta\quad\Longrightarrow\quad u=G$}
{wiki}
The impulse response records the response to a unit impulse, with specified initial or boundary conditions. In continuous time the impulse is a <Dirac delta function>; in discrete time it is the <Kronecker delta> $\delta[n]$. For a <linear time-invariant system> with zero initial state, the response to a general <input> is its <convolution> with the impulse response. The impulse response of a <causal filter> is zero before the impulse.
For the five-sample <moving average>, a discrete impulse produces $h[n]=1/5$ at $n=0,1,2,3,4$ and zero otherwise. The response lasts five samples, so this is a <finite impulse response> system. Its <frequency response> is the finite sum of the five delayed phase contributions: one short input experiment determines how every sustained sinusoid is filtered.
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