[SOLVED] How the convolution of an input signal and system's impulse response determine output

[blooz]

Why the impulse response has been chosen to compute the output of system by convolution with input signal

 

[Milad-D]

the mathematical prove is in all text-books but intuitively we can say:

Because impulse function has the all frequency component in it in an equal manner( it's frequency representation is 1 at all the frequencies). Therefore when you know the answer of the system to the impulse, this means that you know how the system works for whole of the frequency band.