Metrics and Morphing of Power Spectra

Spectral analysis of time-series has been an important tool of science for a very long time. Indeed, periodicities of celestial events and of weather phenomena sparked the curiosity and imagination of early thinkers in the history of science. More recently, the refined mathematical techniques for spectral analysis of the past fifty years form the basis for a wide range of technological developments from medical imaging to communications. However, in spite of the centrality of a spectral representation of time-series, no universal agreement exists on what is a suitable metric between such representations. In this paper we discuss three alternative metrics along with their application in morphing speech signals. Morphing can be naturally effected via a deformation of power spectra along geodesics of the corresponding geometry. The acoustic effect of morphing between two speakers is documented at a website.