TY - GEN
T1 - Signal analysis, moment problems & uncertainty measures
AU - Karlsson, Johan
AU - Georgiou, Tryphon T.
PY - 2005
Y1 - 2005
N2 - Modern spectral estimation techniques often rely on second order statistics of a time-series to determine a power spectrum consistent with data. Such statistics provide moment constraints on the power spectrum. In this paper we study possible distance functions between spectra which permit a reasonable quantitative description of the uncertainty in moment problems. Typically, there is an infinite family of spectra consistent with given moments. A distance function between power spectra should permit estimating the diameter of the uncertainty family, a diameter which shrinks as new data accumulates. Abstract properties of such distance functions are discussed and certain specific options are put forth. These distance functions permit alternative descriptions of uncertainty in moment problems. While the paper focuses on the role of such measures in signal analysis, moment problems are ubiquitous in science and engineering, and the conclusions drawn herein are relevant over a wider spectrum of problems.
AB - Modern spectral estimation techniques often rely on second order statistics of a time-series to determine a power spectrum consistent with data. Such statistics provide moment constraints on the power spectrum. In this paper we study possible distance functions between spectra which permit a reasonable quantitative description of the uncertainty in moment problems. Typically, there is an infinite family of spectra consistent with given moments. A distance function between power spectra should permit estimating the diameter of the uncertainty family, a diameter which shrinks as new data accumulates. Abstract properties of such distance functions are discussed and certain specific options are put forth. These distance functions permit alternative descriptions of uncertainty in moment problems. While the paper focuses on the role of such measures in signal analysis, moment problems are ubiquitous in science and engineering, and the conclusions drawn herein are relevant over a wider spectrum of problems.
UR - http://www.scopus.com/inward/record.url?scp=33847227288&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33847227288&partnerID=8YFLogxK
U2 - 10.1109/CDC.2005.1583073
DO - 10.1109/CDC.2005.1583073
M3 - Conference contribution
AN - SCOPUS:33847227288
SN - 0780395689
SN - 9780780395688
T3 - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
SP - 5710
EP - 5715
BT - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
T2 - 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Y2 - 12 December 2005 through 15 December 2005
ER -