PHANTOM ZEROS IN CURVE-FITTED FREQUENCY-RESPONSE FUNCTIONS

For complete models, there is an exact equivalence between pole/zero a nd pole/residue representations of transfer functions, but in practice truncation is almost inevitably necessary, in which case the equivale nce breaks down. This paper discusses how extra zeros are typically ad ded into a truncated model to compensate for the effects of out-of-ban d modes, and illustrates their effects. Because compensation is primar ily required on the magnitude of the FRF, these extra zeros, named 'ph antom zeros', are typically arranged in pairs around the frequency axi s, so that half of them have maximum phase properties even when the ph ysical model is minimum phase. The number of phantom zeros required de pends on the separation of the excitation and response points. For a d riving point measurement, where there are virtually as many zeros as p oles, the effects of truncation are very small, whereas at the other e xtreme, with no actual zeros, a correspondingly greater number of phan tom zeros is required to correct the slope of the magnitude of the FRF .