Bayesian interpretation of periodograms

Author

Giovannelli, Jean-François ; Idier, Jérôme

Author_Institution

Lab. des Signaux et Syst., SUPELEC, Gif-sur-Yvette, France

Volume

49

Issue

7

fYear

2001

fDate

7/1/2001 12:00:00 AM

Firstpage

1388

Lastpage

1396

Abstract

The usual nonparametric approach to spectral analysis is revisited within the regularization framework. Both usual and windowed periodograms are obtained as the squared modulus of the minimizer of regularized least squares criteria. Then, particular attention is paid to their interpretation within the Bayesian statistical framework. Finally, the question of unsupervised hyperparameter and window selection is addressed. It is shown that maximum likelihood solution is both formally achievable and practically useful

Keywords

Bayes methods; least squares approximations; maximum likelihood estimation; spectral analysis; Bayesian interpretation; Bayesian statistics; maximum likelihood solution; nonparametric approach; parameter estimation; regularization; regularized least squares criteria; spectral analysis; squared modulus; unsupervised hyperparameter selection; unsupervised window selection; windowed periodograms; Amplitude estimation; Bayesian methods; Books; Fourier transforms; Frequency; Least squares methods; Maximum likelihood estimation; Shape; Signal analysis; Spectral analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.928692

Filename

928692