Geometric Methods for Spectral Analysis

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.