Frequency localising basis functions for wide-band identification

A well known difficulty in system identification over a large bandwidth is the ill-conditioning of the normal matrix. This typically manifests itself as poor or erroneous estimates. Several methods have been proposed in the literature for addressing this issue. However, none appear to give an entirely satisfactory solution. Here we present a novel technique, utilising particular basis functions, aimed specifically at improving the numerical properties of the least squares normal matrix in transfer function estimation over a wide bandwidth. We show that, under some mild assumptions, the achieved condition number is actually independent of the frequency range. Several examples are presented showing the superior performance of the proposed method when applied to wide-band estimation problems.