  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. We show 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, i.e. the system is non-minimum phase. In
this paper we propose a method which enables to determine these zeros, 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.
We demonstrate this 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.

Signal Processing;Applied Physics