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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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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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container_title	IEEE transactions on signal processing
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creator	Sandberg, J. Hansson-Sandsten, M.
description	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.
doi_str_mv	10.1109/TSP.2008.2009892
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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
title	A Comparison Between Different Discrete Ambiguity Domain Definitions in Stochastic Time-Frequency Analysis
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