Optimal stochastic discrete time–frequency analysis in the ambiguity and time-lag domain
Author
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.
Department/s
- Mathematical Statistics
- Statistical Signal Processing Group
Publishing year
2010
Language
English
Pages
2203-2211
Publication/Series
Signal Processing
Volume
90
Issue
7
Links
- 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
Document type
Journal article
Publisher
Elsevier
Topic
- Probability Theory and Statistics
Keywords
- Time-frequency analysis
- Auto Covariance Sequence (ACVS)
- Ambiguity domain
Status
Published
Research group
- Statistical Signal Processing Group
ISBN/ISSN/Other
- ISSN: 0165-1684