Why impulse response Why do people calculate impulse response? Generally systems are designed after modelling the possible input signals and calculating the appropriate filters for the desired outputs. Where does impulse response calculation become important?
Having the impulse response allows one to simplify the input of a sampled linear time-invariant system down to one single unit-magnitude input sample.

It is usually fairly simple to build any time domain input from a single unit input (with a linear combination thereof), and thus, given the impulse response for that single input, the output for any time-domain-described input for that system.  Other basis vectors are possible, but may require more or less work (computational effort) for a given type of description of the input.