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Optimal stochastic discrete time–frequency analysis in the ambiguity and time-lag domain

Sandberg, Johan LU and Sandsten, Maria LU (2010) In Signal Processing 90(7). p.2203-2211
Abstract
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Time-frequency analysis, Auto Covariance Sequence (ACVS), Ambiguity domain
in
Signal Processing
volume
90
issue
7
pages
2203 - 2211
publisher
Elsevier
external identifiers
  • wos:000277543000009
  • scopus:77950188709
ISSN
0165-1684
DOI
10.1016/j.sigpro.2010.01.028
language
English
LU publication?
yes
id
ea8272b3-cec2-4729-81b8-9f5906c8465c (old id 1515137)
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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
date added to LUP
2009-12-14 11:01:37
date last changed
2017-10-01 05:06:50
@article{ea8272b3-cec2-4729-81b8-9f5906c8465c,
  abstract     = {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.},
  author       = {Sandberg, Johan and Sandsten, Maria},
  issn         = {0165-1684},
  keyword      = {Time-frequency analysis,Auto Covariance Sequence (ACVS),Ambiguity domain},
  language     = {eng},
  number       = {7},
  pages        = {2203--2211},
  publisher    = {Elsevier},
  series       = {Signal Processing},
  title        = {Optimal stochastic discrete time–frequency analysis in the ambiguity and time-lag domain},
  url          = {http://dx.doi.org/10.1016/j.sigpro.2010.01.028},
  volume       = {90},
  year         = {2010},
}