Phase response reconstruction for non-minimum phase systems using frequency-domain magnitude values

It is often more complicated to measure the phase response of a large system than the magnitude. In that case, one can attempt to use the Kramers-Kronig (KK) relations for magnitude and phase, which relates magnitude and phase analytically. The advantage is that then only the magnitude of the frequency response needs to be measured. It is shown that the KK relations for magnitude and phase may yield invalid results when the transfer function has zeros located in the right half of the complex s-plane, that is, the system is non-minimum phase. In this paper, a method which enables to determine these zeros is proposed, by using specific excitation signals and measuring the resulting time responses of the system. The method is verified using blind tests among the authors. When the locations of the zeros in the right half of the complex s-plane are known, modified KK relations can be successfully applied to non-minimum phase systems. This is demonstrated by computing the phase response of the electric field, excited by a point dipole source inside a closed cavity with Perfect Electrically Conducting (PEC) walls. Also, the effects of simulated measurement noise are considered for this example.

Automated summary

The paper discusses the challenges of measuring the phase response of large systems compared to magnitude response, and proposes using KK relations to relate magnitude and phase. It also presents a method to determine the locations of zeros in the right half of the complex plane for non-minimum phase systems, allowing for successful application of modified KK relations for phase response calculations.