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A Comparison Between Different Discrete Ambiguity Domain Definitions in Stochastic Time-Frequency Analysis

Sandberg, Johan LU and Sandsten, Maria LU (2009) In IEEE Transactions on Signal Processing 57(3). p.868-877
Abstract
The ambiguity domain plays a central role in estimating the time-varying spectrum and in estimating the covariance function of nonstationary random processes in continuous time. For processes in discrete time, there exist different definitions of the ambiguity domain, but it is well known that neither of these definitions perfectly resembles the usefulness of the continuous ambiguity domain. In this paper, we present some of the most frequently used definitions of the ambiguity domain in discrete time: the Claasen-MecklenbrÄuker, the Jeong-Williams, and the Nuttall definitions. For the first time, we prove their equivalence within some necessary conditions and we present theorems that justify their usage.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Ambiguity domain, covariance function estimation, Claasen-Mecklenbräuker, discrete-time discrete-frequency, Nuttall, Jeong–Williams, nonstationary random processes, time-frequency analysis
in
IEEE Transactions on Signal Processing
volume
57
issue
3
pages
868 - 877
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000263431900005
  • scopus:61549132521
ISSN
1053-587X
DOI
10.1109/TSP.2008.2009892
language
English
LU publication?
yes
id
076a3fbd-bc49-40e4-ae4a-ceeabf9ba697 (old id 1301835)
date added to LUP
2009-03-02 13:26:00
date last changed
2017-03-13 13:12:14
@article{076a3fbd-bc49-40e4-ae4a-ceeabf9ba697,
  abstract     = {The ambiguity domain plays a central role in estimating the time-varying spectrum and in estimating the covariance function of nonstationary random processes in continuous time. For processes in discrete time, there exist different definitions of the ambiguity domain, but it is well known that neither of these definitions perfectly resembles the usefulness of the continuous ambiguity domain. In this paper, we present some of the most frequently used definitions of the ambiguity domain in discrete time: the Claasen-MecklenbrÄuker, the Jeong-Williams, and the Nuttall definitions. For the first time, we prove their equivalence within some necessary conditions and we present theorems that justify their usage.},
  author       = {Sandberg, Johan and Sandsten, Maria},
  issn         = {1053-587X},
  keyword      = {Ambiguity domain,covariance function estimation,Claasen-Mecklenbräuker,discrete-time discrete-frequency,Nuttall,Jeong–Williams,nonstationary random processes,time-frequency analysis},
  language     = {eng},
  number       = {3},
  pages        = {868--877},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Signal Processing},
  title        = {A Comparison Between Different Discrete Ambiguity Domain Definitions in Stochastic Time-Frequency Analysis},
  url          = {http://dx.doi.org/10.1109/TSP.2008.2009892},
  volume       = {57},
  year         = {2009},
}