The spectral envelope and its applications

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 evi- dent. In this article we explain the basic concept and give numerous ex- amples of the usefulness of the technology. These examples include anal- yses 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.

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