# Basic question: Why is the output of a system the convolution between the impulse response and the input?

I forgot a very simple fact and I am now struggling to find reference that proves this basic property?

How would you prove that for a single in single out system, the system output is the impulse response convoluted with the input?

• Note that this is only true for linear time invariant systems. – MBaz Feb 11 '15 at 1:46
• This has been answered quite a few times on this site. Have a look at e.g. this and this answer. – Matt L. Feb 11 '15 at 9:21