The periodogram envelope in parametric and non-parametric spectral estimation

The role of the periodogram envelope as a nonparametric approach for spectral estimation and its potential in parametric spectral estimation using variational approaches are examined. The spectral envelope, or its prior estimate the periodogram envelope, represents a very good candidate for starting any approach to spectral estimation due to its smooth character, its robustness against flat noise spectra, and its statistical stability. Setting envelope constraints in variational spectral estimation increases the statistical stability of the resulting estimate while preserving the high resolution of the best reported methods. The case of line spectra is briefly described to demonstrate the potential of the envelope-associated matrix in the line spectrum. This allows the designer to convert SUD and MUSIC methods to the new starting function