Effect of the finite memory length of a recorder in evaluating its frequency response from step response

The length of the record containing the step response of a system affects the estimate of the frequency response obtained from it by the discrete Fourier transform algorithms. An evaluation of the error due to the record truncation is presented in a theoretical case. The amplitude of this error is particularly significant when a small aberration (of the order of a few percent) of the response is considered. A criterion of obtaining the frequency response of a system based on two or more records of the step response acquired with different sampling frequencies is presented. The quantification of the errors in this estimate is discussed, in particular for the low-frequency sampled records. The method is applied to experimental data to estimate the frequency response of an oscilloscope.