Computational technique for the application of the Hilbert transform to frequency domain electrical impedance data

Abstract

A microcomputer program is described that uses the Hilbert transform to transform real data to imaginary and vice-versa in the frequency domain. This is achieved via specific integrals embodied in the Kramers?Kronig relationships. Cubic splines are applied to the measured data to interpolate 100 points per logarithmic decade. The Hilbert transform is computed at each frequency by applying the finite difference form of the algorithm over each logarithmic decade and then summing results for all decades. Two estimates of error are provided. One is a measure of the percentage error for each generated point relative to the measured data; the second is the chi-squared parameter.