A unified approach to nonparametric spectrum estimation algorithms

Different approaches to spectrum estimation can be broadly classified as parametric and nonparametric methods. In the parametric techniques, an underlying model is assumed in the formulation of the spectrum estimation problem and one estimates the parameters of the model. For nonparametric methods, no such model is assumed. In this paper, several nonparametric spectrum estimation algorithms are brought under a unified framework by the introduction of a generalized nonparametric spectrum estimation algorithm. A four-stage approach is employed. It contains as special cases the Blackman-Tukey algorithm, the weighted, overlapped segment averaging (WOSA) method, the lag-reshape approach, Rader's algorithm, and the short-time unbiased spectrum estimation (STUSE) algorithm. The framework proposed in the paper is more general than the one recently proposed by Nuttall and Carter. Theoretical expressions for the spectrum estimation variance of the generalized algorithm are derived, and then verified via simulation example. Also, several nonparametric approaches for obtaining unbiased spectrum estimates are discussed and compared. Finally we conclude the paper with a brief discussion of the applicability and usefulness of several methods in specific situations.