Assessing the accuracy of wideband electrical data using Hilbert transforms

A novel technique for checking the accuracy of wideband electrical measurement data is presented, based on the Hilbert transform relationship between the real and imaginary parts of a complex function. Fundamental properties of the transform are summarised and the convergence of the numerical integration process considered and illustrated. Functions E₁( omega ) and E₂( omega ) are identified as possible indicators of the intrinsic errors in the data and various examples are given to examine the effects of curve fitting, sharp responses statistically dependent and independent random errors and mathematically generated data. It is concluded that with specialist interpretation the new technique can be a valuable checking tool in some wideband measurement programmes, particularly when the typical cost of the latter are considered.