High-Resolution Nonparametric Spectral Analysis: Theory and Applications

Abstract

Spectral estimation can be defined as the art of recovering the frequency content in a measured signal, and is a highly relevant problem in practice. In particular, many engineering problems, ranging from synthetic aperture radar (SAR) imaging to the analysis of time-series observed in seismology or astronomy, can be cast as a spectral analysis problem. A nonparametric spectral estimator is a method that, unlike parametric methods, attempts to compute the spectral content of a signal without using any a priori information or making any explicit assumption about it. While many smoothed versions of the discrete Fourier transform can be interpreted as nonparametric methods, a body of recent work has suggested more advanced such methods that are based on adaptive filterbanks. This chapter provides a review of some of the existing work in the area of nonparametric spectral estimation, including fast implementations of the most successful estimators as well as various extensions to spectral analysis of incomplete data. Numerical examples are provided to exemplify the various algorithms.