Phantom zeros in curve-fitted frequency response functions

Abstract

For complete models, there is an exact equivalence between pole/zero and pole/residue representations of transfer functions, but in practice truncation is almost inevitably necessary, in which case the equivalence breaks down. This paper discusses how extra zeros are typically added into a truncated model to compensate for the effects of out-of-band modes, and illustrates their effects. Because compensation is primarily required on the magnitude of the FRF, these extra zeros, named 'phantom zeros', are typically arranged in pairs around the frequency axis, so that half of them have maximum phase properties even when the physical model is minimum phase. The number of phantom zeros required depends on the separation of the excitation and response points. For a driving point measurement, where there are virtually as many zeros as poles, the effects of truncation are very small, whereas at the other extreme, with no actual zeros, a correspondingly greater number of phantom zeros is required to correct the slope of the magnitude of the FRF.