Summary: IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 44, NO. 10, OCTOBER 1996 1621
Interpolation/Extrapolation of Fre uency Domain
Responses Using the Hilbert Transform
Sharath M. Narayana, Girish Rao, Raviraj Adve, Student Member, IEEE, Tapan K. Sarkar, Fellow, IEEE,
Vincent C. Vannicola, Fellow, IEEE, Michael C. Wicks, Senior Member, IEEE, and Steven A. Scott, Member, IEEE
Abstruct- The Hilbert transform relates the real and the
imaginary parts of the transfer function of a causal system. The
objective of this paper is to illustrate how the Hilbert transform
relationship can be utilized to interpolate/extrapolate measured
frequency domain responses of devices. Sample numerical exam-
ples are presented to illustrate the efficacy of this method.
YSTEM measurements in the time domain are easier
Sto perform since the waveforms of interest are all real.
However, one disadvantage of performing measurements in
the time domain is limited dynamic range. Frequency domain
measurement equipment benefits from large dynamic range.
Furthermore, frequency domain measurements may be carried
out either over an entire range of frequencies or selectively
over a band of frequencies. Theoretically, it is possible to