Comparison of several methods for obtaining the time response of linear systems to either a unit impulse or arbitrary input from frequency-response data

Several methods of obtaining the time response of linear systems to either a unit impulse or an arbitrary input from frequency-response data are described and compared. Comparisons indicate that all the methods give good accuracy when applied to a second-order system; the main difference is the required computing time. Several of the methods when applied to higher order systems require excessive computing time in order to obtain the same degree of accuracy. The methods generally classified as inverse Laplace transform methods were found to be most effective in determining the response to a unit impulse from frequency-response data of higher order systems. Some discussion and examples are given of the use of the methods as flight-data-analysis techniques in predicting loads and motions of a flexible aircraft on the basis of simple calculations when the aircraft frequency response is known.