The relation between discrete periodic inputs, the transfer function and the transient response of a system

Sampled-data systems are characterized by the presence of discrete signals at some point of the system, but the overall output is usually a continuous function of time. It is shown that the pulse sequence of discrete periodic signals, which result in a finite-settling-time response when applied to the input of a system, can be determined directly from the system transient response. Such a pulse sequence can be used to design a discrete controller to compensate the system, when its transfer function is not known. Further, it is shown that the transfer function of a system can be found once an input pulse sequence has been determined, with an accuracy limited only by the accuracy of the given transient response.