Optimal stochastic discrete time–frequency analysis in the ambiguity and time-lag domain
Författare
Summary, in English
In stochastic time-frequency analysis, the covariance function is often estimated from only one observed realization with the use of a kernel function. For processes in continuous time, this can equivalently be done in the ambiguity domain, with the advantage that the mean square error optimal ambiguity kernel can be computed. For processes in discrete time, several ambiguity domain definitions have been proposed. It has previously been reported that in the Jeong-Williams ambiguity domain, in contrast to the Nutall and the Claasen-Mecklenbräucker ambiguity domain, any smoothing covariance function estimator can be represented as an ambiguity kernel function. In this paper, we show that the Jeong-Williams ambiguity domain can not be used to compute the mean square error (MSE) optimal covariance function estimate for processes in discrete time. We also prove that the MSE optimal estimator can be computed without the use of the ambiguity domain, as the solution to a system of linear equations. Some properties of the optimal estimator are derived.
Avdelning/ar
- Matematisk statistik
- Statistical Signal Processing Group
Publiceringsår
2010
Språk
Engelska
Sidor
2203-2211
Publikation/Tidskrift/Serie
Signal Processing
Volym
90
Issue
7
Länkar
- Publication in Lund University research portal
- http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V18-4YB5M0J-1-7&_cdi=5668&_user=745831&_pii=S0165168410000459&_orig=search&_coverDate=07%2F31%2F2010&_sk=999099992&view=c&wchp=dGLzVzz-zSkWb&_valck=1&md5=d0027f54d4a1924ba35552da27787c20&ie=/sdarticle.pdf
- http://dx.doi.org/10.1016/j.sigpro.2010.01.028
Dokumenttyp
Artikel i tidskrift
Förlag
Elsevier
Ämne
- Probability Theory and Statistics
Nyckelord
- Time-frequency analysis
- Auto Covariance Sequence (ACVS)
- Ambiguity domain
Status
Published
Forskningsgrupp
- Statistical Signal Processing Group
ISBN/ISSN/Övrigt
- ISSN: 0165-1684