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added math-physics tag, since this more a question of physics than of maths
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Why is the output of an LTI system the convolution of the input funtion and the impulse response?I am looking at the description of LTI systems in the time domain. Intuitively, I'd have guessed it would be the composition of the input function and some "system function". $$ y(t) = f(x(t)) = (f\circ x)(t)$$ Where $x(t)$ is the input, $y(t)$ output and $f(x)$ a "system function". Why is it not that way? Could such a "system function" be found for, say, an R-C-Circuit? The actual output function y(t), is defined as $$ y(t) = (h * x)(t) $$ Where $h(t)$ is the response to a dirac impulse. This is hard to grasp for me. Why is it so? I have looked at various explanations, drawings of rectangles becoming infinitely narrow, which I sort of understood, but it is still "hard to grasp"! I am looking for a simple explanation in one or two sentences here.
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