Bounds on frequency response estimates derived from uncertain step response data

The frequency response of a system can be estimated from measurements of its step response; however, many error sources affect the accuracy of such estimates. This paper investigates the effects of uncertainty in the knowledge of the step response. Methods for establishing uncertainty bounds for the frequency response estimates are developed, based on the corresponding time-domain uncertainties associated with the measured step response. Two methods are described. One method produces bounds that are often very conservative. The other method produces bounds that are more realistic. End effects that influence the bounds are also considered. A simulation example and an application of the bounds are presented