An Interpretation of the Dual Problem of the THREE-like Approaches

TL;DR

This paper interprets the dual problem in THREE-like spectral estimation as a new parametric estimation problem, revealing the optimality of solutions in terms of closeness to the correlogram within a spectral density class.

Contribution

It provides a novel interpretation of the dual problem in THREE-like spectral estimation, linking it to a parametric estimation framework and enhancing understanding of its optimality.

Findings

Dual problem viewed as a new parametric spectral estimation problem

THREE-like solutions are optimal relative to the correlogram within a spectral class

Enriches the theoretical understanding of spectral estimation methods

Abstract

Spectral estimation can be preformed using the so called THREE-like approach. Such method leads to a convex optimization problem whose solution is characterized through its dual problem. In this paper, we show that the dual problem can be seen as a new parametric spectral estimation problem. This interpretation implies that the THREE-like solution is optimal in terms of closeness to the correlogram over a certain parametric class of spectral densities, enriching in this way its meaningfulness.