lnu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Gabor discretization of the Weyl product for modulation spaces and filtering of nonstationary stochastic processes
Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia.
Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia.
2009 (English)In: Applied and Computational Harmonic Analysis, ISSN 1063-5203, E-ISSN 1096-603X, Vol. 26, no 1, 97-120 p.Article in journal (Refereed) Published
Abstract [en]

We discretize the Weyl product acting on symbols of modulation spaces, using a Gabor frame defined by a Gaussian function. With one factor fixed. the Weyl product is equivalent to a matrix multiplication on the Gabor coefficient level. If the fixed factor belongs to the weighted Sjostrand space M omega(infinity,1), then the matrix has polynomial or exponential off-diagonal decay, depending oil the weight omega. Moreover, if its operator is invertible on L(2), the inverse matrix has similar decay properties. The results are applied to the equation for the linear minimum mean square error filter for estimation of a nonstationary second-order stochastic process from a noisy observation. The resulting formula for the Gabor coefficients of the Weyl symbol for the optimal filter may be interpreted as a time-frequency version of the filter for wide-sense stationary processes, known as the noncausal Wiener filter.

Place, publisher, year, edition, pages
Amsterdam: Elsevier, 2009. Vol. 26, no 1, 97-120 p.
National Category
Mathematical Analysis
Research subject
Mathematics, Applied Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-27584DOI: 10.1016/j.acha.2008.02.005OAI: oai:DiVA.org:lnu-27584DiVA: diva2:637386
Available from: 2013-07-17 Created: 2013-07-17 Last updated: 2013-07-29Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Wahlberg, Patrik
In the same journal
Applied and Computational Harmonic Analysis
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 45 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf