convolution sum

rwsignal

q:: Any LTI system can be characterized completely in terms of its response to a unit impulse.

$x[n]={\sum }_{k=-\infty }^{\infty }x[k]\delta [n-k]$ s

sifting property

This property states that any discrete-time signal, x[n], can be represented as a sum of scaled and shifted unit impulses (δ[n−k]).

Response of LTI to unit impulse