Adaptive smoothing of Frequency Response Functions in Digital Spectral Analysers

We claim in this paper that, in many applications, the non-parametric measurement of frequency response functions can be greatly improved by adaptive smoothing in the frequency domain. Adaptive smoothing aims at finding the optimal balance between bias and variance errors at any frequency, depending on whether accuracy or precision is locally of concern. Our approach is based on a generalisation of the weighted overlapped segment averaging procedure, such as currently used in digital spectral analysers, but where additional cross-correlations between segments are allowed for. The number of significant cross-correlations to be accounted for, at a given frequency, automatically and optimally specifies the "degree of smoothness" required by the FRF measurement. Among the many possible routes leading to the design of adaptive smoothers, our approach is dictated by the requirement of having an implementation that departs little from that currently in use in digital spectral analysers.