This paper explores a geometric framework for modeling nonstationary but slowly varying time series, based on the assumption that short-windowed power spectra capture their spectral character, and that energy transference in the frequency domain has a physical significance. The framework relies on certain notions of transportation distance and their respective geodesics to model possible nonparametric changes in the power spectral density with respect to time. We discuss the relevance of this framework to applications in spectral tracking, spectral averaging, and speech morphing.
Bibliographical noteFunding Information:
Manuscript received May 27, 2011; revised October 04, 2011; accepted November 23, 2011. Date of publication December 08, 2011; date of current version February 10, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Peter J. Schreier. This work was supported by the National Science Foundation, the Vincentine Hermes-Luh endowment, the Digital Technology Center, University of Minnesota, and the Air Force Office of Scientific Research.
- spectral analysis
- spectral averaging
- spectral metrics
- spectral tracking
- speech morphing
- transportation distance