Frequency response from transient-response data

H. Thal-Larsen
1955 Electrical Engineering  
This work explains how to obtain the unit step time domain response by means of the frequency response of a regulator (gain and phase) using the Floyd's Modified Computational Method. The preliminary condition is that the gain of the system tends to zero as the frequency tends to infinite. Floyd's Method uses the Fourier's Inverse Transform to achieve the Impulse Unit response. The Modified Method calculates the integral. This work details the mathematical developnent of Floyd's Method. Authors
more » ... introduce the integral of the Impulse Unit response to obtain the Step Unit response and also the linearization of the Method in order to approximate it and obtain an equation to do the computational calculation. We apply the modified method in a second order system, calculating its frequency response and its analytic step unit response by means of the MNatlab. Then we use the equation developed in this work by the linearization of Floyd's Modified Method applied in the frequency response of the system and compare with the step unit analytic response. The relative error is calculated and we can observe that Floyd's Modified Method generates a step unit response in the time domain that has some time little retard and with values a little inferior to the analytic response. This behavior is attributed to the linearization and to do not use the complete frequency band of the system. However the final values are very exact. T.
doi:10.1109/ee.1955.6439423 fatcat:tuawfak5n5gyfbtdh5pvd3ax6e