Spectrum estimation and harmonic analysis

Citations Over TimeTop 10% of 1982 papers

Abstract

In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," are dominant. In this paper we present a new method based on a "local" eigenexpansion to estimate the spectrum in terms of the solution of an integral equation. Computationally this method is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows (discrete prolate spheroidal sequences) to treat both the bias and smoothing problems. Some of the attractive features of this estimate are: there are no arbitrary windows; it is a small sample theory; it is consistent; it provides an analysis-of-variance test for line components; and it has high resolution. We also show relations of this estimate to maximum-likelihood estimates, show that the estimation capacity of the estimate is high, and show applications to coherence and polyspectrum estimates.

Related Papers

• → Time Series in the Frequency Domain(1983)38 cited
• → Estimation of cross-power and auto-power spectral densities in frequency domain by subspace methods(2012)9 cited
• → Coherence Modified for Sensitivity to Relative Phase of Real Band-Limited Time Series(2014)2 cited
• → Efficient Spectral Analysis Of Quasi Stationary Time Series(2007)
• → Spectral Analysis and Linear Filters(2016)