Application of generalized linear filters in data analysis

Stewart Barnes, M. Peter, L. Hoffmann, A. A. Manuel, A. Shukla

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

It is shown that a useful generalized linear filter W can be constructed from experimental data. The data are divided into many experiments and this ensemble is used to calculate the autocorrelation functions which appear in W. In turn, from this filter one determines a "Hamiltonian" ℋ. The eigenvectors and eigenvalues of this Hamiltonian are evaluated. For a "good" experiment there is one small eigenvalue, and the rest are ≈1. The W so determined usefully reduces the noise in a new data set. The presence of two or more small eigenvalues indicates that the experimental data contains more than a single signal. The action of W on selected members of the ensemble, and/or new data sets, extracts the different signals with, again, a useful noise reduction. Both computer simulations and real positron annihilation data are used to illustrate these development.

Original languageEnglish (US)
Pages (from-to)679-701
Number of pages23
JournalJournal of Statistical Physics
Volume76
Issue number1-2
DOIs
StatePublished - Jul 1994

Fingerprint

linear filters
Linear Filter
Data analysis
eigenvalues
Smallest Eigenvalue
Ensemble
Experimental Data
positron annihilation
noise reduction
autocorrelation
Eigenvalues and Eigenvectors
Noise Reduction
eigenvectors
Autocorrelation Function
computerized simulation
Annihilation
Experiment
filters
Computer Simulation
Filter

Keywords

  • data analysis
  • Generalized linear filters
  • image processing

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Application of generalized linear filters in data analysis. / Barnes, Stewart; Peter, M.; Hoffmann, L.; Manuel, A. A.; Shukla, A.

In: Journal of Statistical Physics, Vol. 76, No. 1-2, 07.1994, p. 679-701.

Research output: Contribution to journalArticle

Barnes, S, Peter, M, Hoffmann, L, Manuel, AA & Shukla, A 1994, 'Application of generalized linear filters in data analysis', Journal of Statistical Physics, vol. 76, no. 1-2, pp. 679-701. https://doi.org/10.1007/BF02188681
Barnes, Stewart ; Peter, M. ; Hoffmann, L. ; Manuel, A. A. ; Shukla, A. / Application of generalized linear filters in data analysis. In: Journal of Statistical Physics. 1994 ; Vol. 76, No. 1-2. pp. 679-701.
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