Impulse Response: mathematically the impulse response can be modeled as a dirac delta function. The dirac delta represents an infinitely short pulse that has an infinitely high peak. The function itself exists as a mathematical object only when present in an integral. It is a measure that approximates the 0 value of the function that it multiplies with in the integral. The dirac delta function can be used to solve differential equations, because the convolution of a function with the delta function is itself.
