Approximation of transient response

ALTHOUGH FEEDBACK CONTROL design requirements usually specify the output time response to some standard form of input, the design process commonly is performed on a frequency response basis. The existing wealth of knowledge and experience in steady-state a-c circuit theory and in feedback amplifier performance justifies this design procedure. Under these conditions the need to transform from the frequency to the time domain is great. Exact mathematical methods of performing the desired transformation for linear systems exist but unfortunately do not lead to closed form results except in very special cases. Since even completely random inputs may be considered as composed of successions of impulses, knowledge of impulse response leads easily to the response for any specified input.