Ambiguity Domain Definitions and Covariance Function Estimation for NonStationary Random Processes in Discrete Time
(2008) Abstract
 The ambiguity domain plays a central role in estimating the timevarying spectrum of a nonstationary random process in continuous time, since multiplication in this domain is equivalent with estimating the covariance function of the random process using an intuitively appealing estimator. For processes in discrete time there exists a corresponding covariance function estimator. The ambiguity domain was originally defined for processes in continuous time and by its construction it is not trivial to define a similar concept for processes in discrete time. Several different definitions have been proposed. In Paper A we examine three of the most frequently used definitions and prove that only one of them has the important property that... (More)
 The ambiguity domain plays a central role in estimating the timevarying spectrum of a nonstationary random process in continuous time, since multiplication in this domain is equivalent with estimating the covariance function of the random process using an intuitively appealing estimator. For processes in discrete time there exists a corresponding covariance function estimator. The ambiguity domain was originally defined for processes in continuous time and by its construction it is not trivial to define a similar concept for processes in discrete time. Several different definitions have been proposed. In Paper A we examine three of the most frequently used definitions and prove that only one of them has the important property that multiplication is equivalent with the mentioned covariance function estimator. Another useful property of the continuous ambiguity domain is that the mean square error optimal covariance function estimator has an attractive formulation in this domain. In Paper B we prove that none of the three examined ambiguity domain definitions for discrete processes has this property. However, we prove that the optimal estimator can be computed without the use of the ambiguity domain for processes in discrete time. In Paper C we prove that the mean square error optimal covariance function estimator of the form discussed in this thesis, can be computed for any parameterized family of random processes as the solution to a system of linear equations. Examples of families and their corresponding optimal estimators are given. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1259798
 author
 Sandberg, Johan ^{LU}
 supervisor

 Maria Sandsten ^{LU}
 organization
 publishing date
 2008
 type
 Thesis
 publication status
 published
 subject
 language
 English
 LU publication?
 yes
 id
 eb58bc4886304aeb9b62e863f045ba96 (old id 1259798)
 date added to LUP
 20090525 16:22:57
 date last changed
 20160919 08:45:00
@misc{eb58bc4886304aeb9b62e863f045ba96, abstract = {The ambiguity domain plays a central role in estimating the timevarying spectrum of a nonstationary random process in continuous time, since multiplication in this domain is equivalent with estimating the covariance function of the random process using an intuitively appealing estimator. For processes in discrete time there exists a corresponding covariance function estimator. The ambiguity domain was originally defined for processes in continuous time and by its construction it is not trivial to define a similar concept for processes in discrete time. Several different definitions have been proposed. In Paper A we examine three of the most frequently used definitions and prove that only one of them has the important property that multiplication is equivalent with the mentioned covariance function estimator. Another useful property of the continuous ambiguity domain is that the mean square error optimal covariance function estimator has an attractive formulation in this domain. In Paper B we prove that none of the three examined ambiguity domain definitions for discrete processes has this property. However, we prove that the optimal estimator can be computed without the use of the ambiguity domain for processes in discrete time. In Paper C we prove that the mean square error optimal covariance function estimator of the form discussed in this thesis, can be computed for any parameterized family of random processes as the solution to a system of linear equations. Examples of families and their corresponding optimal estimators are given.}, author = {Sandberg, Johan}, language = {eng}, note = {Licentiate Thesis}, title = {Ambiguity Domain Definitions and Covariance Function Estimation for NonStationary Random Processes in Discrete Time}, year = {2008}, }