So this is just discrete convolution but continuous time convolution AFAIK has no intuitive explanation. The general idea is there is a sense of taking mathema

So this is just discrete convolution but continuous time convolution AFAIK has no intuitive explanation. The general idea is there is a sense of taking mathematical operations as having not just numbers and variables and outputing another number or variable... but that operations can take any number of anything and output any number of anything. The Fourier Transform takes in a function and outputs another function, which you can put meaning on it or you can just "nod and continue" (which is often easier instead of trying to put some words on abstract concepts). Some "ideas" you can use to analyze the situation are concepts learned in things like linear algebra like abstract vector spaces, basis, eigen-whatever... and so on. In the case of the continuous time convolution, it just turns out there is a magical thing associated with something called a Dirac Delta function with certain properties that are important for various things in controls engineering. Kinda feels like a piece of turd that refuses to evacuate but I just stopped caring about "intuitive" explanations.