Numerical Fourier Transform Calculations for Pulse Testing Procedures

Abstract

Pulse testing of systems, where the input is a controlled function of time, is a well-established procedure. One data reduction technique numerically calculates the Fourier transforms of the input and the response. The complex ratio is the FT of the system function. It is shown (a) that the correction function usually employed to improve the respective FTs cancels out and is a useless operation; (b) that the numerical system function FT fails at high frequencies because the approximation to the integral fails to converge; (c) the upper limit in frequency is ωδ ≤ 0.1π, not π as predicted by the sampled data theorem; (d) generally it is necessary to use ten times as many data points as has been the practice to attain a given bandwidth.