Bounds on frequency response estimates derived from uncertain step response data

A system´s frequency response 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 frequency response estimates are developed based on the corresponding time-domain uncertainties associated with the step-like waveform. Two methods are described. One is a provable upper bound that is often very conservative. The other is more realistic, but it is based on an unproved conjecture. End effects that influence the bounds are also considered. A simulated example of the bounds is presented