Hi all. A problem I was working on required that I find the impulse response where I am given the output function ( y(t) ) of a system in terms of the input ( x(t) ). I read somewhere that to find the impulse response, you need a function that relates the output and the input, then you substitute h(t) for every y(t) and δ(t) (the impulse function) for every x(t) then finally solve for h(t) and that would be the impulse response. Assuming what I just stated is correct, my question is why does it work like that? Specifically why does substituting δ(t) for every x(t) lead to the impulse response?