TY - GEN
T1 - Power spectral geodesics and tracking
AU - Jiang, Xianhua
AU - Luo, Zhi Quan
AU - Georgiou, Tryphon T.
PY - 2008
Y1 - 2008
N2 - It is often reasonable to assume that a power spectral density can be used to reflect, locally in time, properties of a non-stationary time series; for instance, the short-time Fourier transform is based on this hypothesis and provides a succession of estimated power spectra over successive time intervals. In this paper we consider such families of power spectral densities, indexed by time, to represent changes in the spectral content of non-stationary processes. We propose as a model for the drift in spectral power over time, the model of mass transport; that is, at least locally, spectral power shifts along geodesics of a suitable mass-transport metric. We show that fitting spectral geodesics in the Wasserstein metric to data is a convex quadratic program. Finally, we highlight the effectiveness of this proposition in tracking features (e.g., spectral lines, peaks) of non-stationary processes.
AB - It is often reasonable to assume that a power spectral density can be used to reflect, locally in time, properties of a non-stationary time series; for instance, the short-time Fourier transform is based on this hypothesis and provides a succession of estimated power spectra over successive time intervals. In this paper we consider such families of power spectral densities, indexed by time, to represent changes in the spectral content of non-stationary processes. We propose as a model for the drift in spectral power over time, the model of mass transport; that is, at least locally, spectral power shifts along geodesics of a suitable mass-transport metric. We show that fitting spectral geodesics in the Wasserstein metric to data is a convex quadratic program. Finally, we highlight the effectiveness of this proposition in tracking features (e.g., spectral lines, peaks) of non-stationary processes.
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U2 - 10.1109/CDC.2008.4739291
DO - 10.1109/CDC.2008.4739291
M3 - Conference contribution
AN - SCOPUS:62949195755
SN - 9781424431243
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 1315
EP - 1319
BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 47th IEEE Conference on Decision and Control, CDC 2008
Y2 - 9 December 2008 through 11 December 2008
ER -