Optimal stochastic discrete time–frequency analysis in the ambiguity and time-lag domain
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1515137
- author
- Sandberg, Johan LU and Sandsten, Maria LU
- organization
- publishing date
- 2010
- 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)
- alternative location
- 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
- 2016-04-04 10:06:19
- date last changed
- 2022-01-29 19:48:16
@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}},
keywords = {{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}},
doi = {{10.1016/j.sigpro.2010.01.028}},
volume = {{90}},
year = {{2010}},
}