TY - JOUR
T1 - HILBERT TRANSFORMS FROM INTERPOLATION DATA.
AU - Parker, Philip J.
AU - Anderson, Brian D.O.
PY - 1987
Y1 - 1987
N2 - The authors study the generation of stable transfer functions for which the real or imaginary part takes prescribed values at discrete uniformly spaced points on the unit circle. Formulas bounding the error between a particular interpolating function and any function consistent with the data are presented, which have the desirable property that the error goes to zero exponentially fast with the number of interpolating points. The generation of stable minimum-phase transfer functions for which the magnitude takes prescribed values at uniformly spaced points on the unit circle is examined, and error bounds for this problem are presented. A connection with the discrete Hilbert transform is made. The effect of uncertainty in the original data is examined.
AB - The authors study the generation of stable transfer functions for which the real or imaginary part takes prescribed values at discrete uniformly spaced points on the unit circle. Formulas bounding the error between a particular interpolating function and any function consistent with the data are presented, which have the desirable property that the error goes to zero exponentially fast with the number of interpolating points. The generation of stable minimum-phase transfer functions for which the magnitude takes prescribed values at uniformly spaced points on the unit circle is examined, and error bounds for this problem are presented. A connection with the discrete Hilbert transform is made. The effect of uncertainty in the original data is examined.
UR - http://www.scopus.com/inward/record.url?scp=0023604161&partnerID=8YFLogxK
U2 - 10.1109/cdc.1987.272632
DO - 10.1109/cdc.1987.272632
M3 - Conference article
AN - SCOPUS:0023604161
SN - 0191-2216
SP - 1350
EP - 1355
JO - Proceedings of the IEEE Conference on Decision and Control
JF - Proceedings of the IEEE Conference on Decision and Control
ER -