Uncertainties of frequency response estimates derived from responses to uncertain step-like inputs

The frequency response of a linear time-invariant system can be estimated from the measurement of its response to an ideal step input. However, an ideal step is unrealizable, and various other error sources affect the accuracy of such estimates. This paper investigates the effect of using an uncertain (inexactly known), step-like test signal. An approach is developed here for determining the systematic uncertainties of the frequency response estimate of a device under test (DUT), when it is estimated from the response of the DUT to the uncertain, step-like test signal. The time-domain uncertainties of the test signal, and those of the DUT response, are converted to the frequency domain and processed, resulting in uncertainties for the frequency response of the DUT. Also, a mathematical proof is provided for the “envelope-modulation” method of calculating the systematic uncertainties of a frequency response estimate of a device, as derived from the uncertain response of the device to an ideal step