Paper Info
Title
Welch method revisited: nonparametric power spectrum estimation via circular overlap
Abstract
The objective of this paper is twofold. The first part provides further insight in the statistical properties of the Welch power spectrum estimator. A major drawback of the Welch method reported in the literature is that the variance is not a monotonic decreasing function of the fraction of overlap. Selecting the optimal fraction of overlap, which minimizes the variance, is in general difficult since it depends on the window used. We show that the explanation for the nonmonotonic behavior of the variance, as reported in the literature, does not hold. In the second part, this extra insight allows one to eliminate the nonmonotonic behavior of the variance for the Welch power spectrum estimator (PSE) by introducing a small modification to the Welch method. The main contributions of this paper are providing extra insight in the statistical properties of the Welch PSE; modifying the Welch PSE to circular overlap--the variance is a monotonically decreasing function of the fraction of overlap, making the method more user friendly; and an extra reduction of variance with respect to the Welch PSE without introducing systematic errors--this reduction in variance is significant for a small number of data records only.
Year
DOI
Venue
2010
10.1109/TSP.2009.2031724
IEEE Transactions on Signal Processing
Keywords
Field
DocType
overlap,extra reduction,welch's method,windowing,optimal fraction,welch method,wosa method.,welch pse,index terms—nonparametric,small number,statistical property,welch power spectrum estimator,nonmonotonic behavior,small modification,system identification,power spectrum,extra insight,variance reduction,nonparametric power spectrum estimation,estimation theory,statistical analysis,signal processing,transfer functions,nonparametric,speech recognition,welch s method,frequency,indexing terms
Monotonic function,Mathematical optimization,Algorithm,Nonparametric statistics,Welch's method,Spectral density,Estimation theory,Statistics,System identification,Variance reduction,Mathematics,Estimator
Journal
Volume
Issue
ISSN
58
2
1053-587X
Citations 
PageRank 
References 
11
0.93
5
Authors
3
Name
Order
Citations
PageRank
Kurt Barbé18120.28
Rik Pintelon21011163.45
Johan Schoukens337658.12