A simple method for calculating the time response of a system to an arbitrary input

THERE are a number of methods for calculating the response of a linear system to an arbitrary input which divide the input into a series of units so small that each can be approximated quite crudely, but they are all quite laborious and require a very high degree of accuracy of computation to achieve adequate accuracy in the calculated response. Even more important, they give very little insight into why the system responds the way it does, or how the system transfer function should be changed to improve the response.