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

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 neith...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2009-03, Vol.57 (3), p.868-877
Main Authors: Sandberg, J., Hansson-Sandsten, M.
Format: Article
Language:English
Subjects:
Ambiguity
Ambiguity domain
Applied sciences
Claasen-MecklenbrÄuker
Councils
Covariance
covariance function estimation
Discrete transforms
discrete-time discrete-frequency
Estimating
Exact sciences and technology
Information, signal and communications theory
Jeong-Williams
Kernel
Matematik
Mathematics
Miscellaneous
Natural Sciences
Naturvetenskap
nonstationary random processes
Nuttall
Probability Theory and Statistics
Random processes
Sannolikhetsteori och statistik
Shape
Signal processing
Statistics
Stochastic processes
Stochasticity
Telecommunications and information theory
Theorems
Time frequency analysis
Visualization
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Description
Summary: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-Mecklenbrauker, 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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2008.2009892