Reconstructing a Nonminimum Phase Response From Amplitude-Only Data of an Electromagnetic System
- February 2, 2018
- Posted by: RSIS
- Categories: Electrical and Electronics Engineering, Engineering
International Journal of Research and Scientific Innovation (IJRSI) | Volume V, Issue I, January 2018 | ISSN 2321–2705
Reconstructing a Nonminimum Phase Response From Amplitude-Only Data of an Electromagnetic System
Kishore Maity and Tapan Kumar Sarkar
Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY, 13244-1240.
Abstract—A general method is presented for reconstructing nonminimum phase from amplitude only data. The nonminimum phase is generated utilizing the nonparametric method.The advantage of this method is that no priori information is needed and no such choice of basis function is required as the solution procedure develops the nature of the solution. This is accomplished by the Hilbert Transform which is a very fundamental property of nature that the real and imaginary part of the nonminimum phase transfer function can satisfy the relationship. The application of this method has been applied to the some antenna radiation pattern and scattering parameters of microwave filters.
Keywords—Nonminimum Phase, Amplitude-only, Hilbert Transform.
I. INTRODUCTION
IN an electromagnetic system, the magnitude response can easily be measured but the phase response is hard to obtain. Thereforeitis importanttoreconstructthe phaseresponsefrom amplitude-onlydata.For minimum phase systems, the reconstruction of phase from amplitude-only data is relatively straightforward as the phase response is given by the Hilbert transform of the log of the magnitude of the amplitude data . In other words, the minimum phase as a function of frequency is given by and is expressed as It can be shown that the minimum phase and the log magnitude of the amplitude have a Hilbert transform relationship. In other words, the minimum phase as a function of frequency w can be expressed as
where P denotes a principal-value integral, as the integrand has a singularity and is not integrable. The integral in (1) only exists in a principal-value sense. However, this property given by (1) of a linear-time invariant system does not hold if the system is not minimum phase.
