Non-minimum phase behavior due to fractional Hilbert transform in broadband circular polarization antennas

2010 ◽  
Author(s):  
H. D. Foltz ◽  
J. S. McLean ◽  
A. Medina ◽  
R. Sutton
Keyword(s):  
Phase Behavior ◽  
Circular Polarization ◽  
Hilbert Transform ◽  
Minimum Phase ◽  
Fractional Hilbert Transform

Fractional Hilbert transform

1996 ◽  
Vol 21 (4) ◽  
pp. 281 ◽  
Author(s):  
Adolf W. Lohmann ◽  
David Mendlovic ◽  
Zeev Zalevsky
Keyword(s):  
Hilbert Transform ◽  
Fractional Hilbert Transform

The Effects of Membrane Properties and Structural Parameters on the Non-Minimum Phase Behavior of the PEM Fuel Cell Humidification System

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
John F. Hall ◽  
Christine A. Mecklenborg ◽  
Clay S. Hearn ◽  
Dongmei Chen
Keyword(s):  
Fuel Cell ◽  
Phase Behavior ◽  
Material Property ◽  
Coupling Effect ◽  
Structural Parameters ◽  
Pem Fuel Cell ◽  
Membrane Properties ◽  
Minimum Phase ◽  
Vapor Transfer ◽  
Channel Plate

The water vapor transfer across a Nafion® membrane exhibits an undesired non-minimum phase behavior. This paper will show that even in the disturbance-to-output loop, the non-minimum phase zero adversely affects the feedback controller design because of the coupling effect between the disturbance-to-output and the input-to-output loops. The non-minimum phase zero location is influenced by the channel plate structure and the membrane material property. The structural parameters examined in this research include channel plate dimensions and heat transfer coefficients. The membrane properties studied include membrane vapor transfer properties described in the Arrhenius’ equation. A governing equation to link the non-minimum phase zero and the parameters is developed in this paper. This equation shows that the non-minimum phase zero arises from the competing heat and mass transfer dynamics, and is determined by the structural parameters and membrane properties. A sensitivity study is presented and shows that structural and material property optimization can be used with the control system design to mitigate the non-minimum phase behavior in the PEM fuel cell humidification system.

CEPSTRUM ALIASING AND THE CALCULATION OF THE HILBERT TRANSFORM

Geophysics ◽  
1974 ◽  
Vol 39 (4) ◽  
pp. 543-544 ◽  
Author(s):  
Paul L. Stoffa ◽  
Peter Buhl ◽  
George M. Bryan
Keyword(s):  
Hilbert Transform ◽  
Phase Function ◽  
Amplitude Spectrum ◽  
Magnetic Data ◽  
Minimum Phase ◽  
Original Function ◽  
Cepstrum Analysis ◽  
Complex Cepstrum ◽  
The Hilbert Transform ◽  
Special Case

Schafer (1969) has pointed out that the Hilbert transform approach used in computing the minimum‐phase spectrum of a given amplitude spectrum corresponds to a special case of complex‐cepstrum analysis in which the phase information of the original function is ignored. The resulting complex cepstrum is an even function. Since a minimum‐phase function has no complex‐cepstrum contributions for T<0, its even part must exactly cancel the odd part for T<0. Thus, by setting all complex‐cepstrum contributions for T<0 equal to zero and doubling all contributions for T>0, we obtain the complex cepstrum of the minimum‐phase function corresponding to the original function. However, the DFT-calculated complex cepstrum is an aliased function (Stoffa et al., 1974). Thus some negative periods will appear at positive locations and vice versa. Appending the original function with zeros will reduce the aliasing. Shuey (1972), in computing the Hilbert transform for magnetic data, indicates that the computation breaks down near the end of the profile, or at long cepstrum periods. This is precisely the point in the even cepstrum where aliasing will have its greatest effect.

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