A numerical method for determining a system impulse response from the transient response to arbitrary inputs

The transfer functions of large physical systems must be known if they are to be controlled efficiently. Environmental transient test procedures are described and their advantages presented. Because impulse and step functions cannot be obtained from practical test equipment, the problem of deducing the impulse response from arbitrary input and response data arises. A successful iteration procedure for determining
h(\tau)
, the impulse response, by using the convolution equation,
r(t) = \int\min{o}\max{\intfy} \Theta(t-\tau) h (\tau) d\tau
, is described. An actual test transient is analyzed. An analog computer technique which mechanizes this iteration procedure is presented. The Appendix contains a tape multiplication procedure for performing numerical convolutions.