The spectral envelope and its applications

Abstract

The concept of the spectral envelope was recently introduced as a statistical basis for the frequency domain analysis and scaling of qualitative-valued time series. In the process of developing the spectral envelope methodology, many other interesting extensions became evident. In this article we explain the basic concept and give numerous examples of the usefulness of the technology. These examples include analyses of DNA sequences, finding optimal transformations for the analysis of real-valued time series, residual analysis, detecting common signals in many time series,and the analysis of textures.