Regeneration of frequency response functions from poles and zeros: a discussion with implications for cepstrum-based operational modal analysis

Operational modal analysis (OMA) seeks to determine a structure’s dynamic characteristics from response-only measurements, which comprise both excitation and transmission path effects. The cepstrum has been used successfully in a number of applications to separate these source and path effects, after which the poles and zeros of the transfer function can be obtained via a curve-fitting process. The contributions from the individual poles and zeros can then be added (in log magnitude) to regenerate the frequency response function (FRF). This paper discusses a number of observations relating to this FRF regeneration process, as well as a number of broader points explaining FRFs from a pole-zero perspective. Among the topics covered in the discussion are: the required distribution of poles and zeros for the successful regeneration of FRFs; node points and weak modes in a pole-zero model; the differences in pole-zero distribution between receptance, mobility and inertance FRF forms; and, how to deal with the very low frequency region when regenerating FRFs. It is hoped that the discussion will assist in the application of cepstrum-based OMA methods and will lead to improved understanding of the FRF regeneration process and of frequency response functions more broadly.