TitleDecorrelation Property of Discrete Wavelet Transform Under Fixed-Domain Asymptotics
Publication TypeJournal Articles
Year of Publication2013
AuthorsChang, X, Stein, ML
JournalIEEE Transactions on Information Theory
Volume59
Pagination8001-8013
Date Published2013
KeywordsSupply Chain
Abstract

Theoretical aspects of the decorrelation propertyof the discrete wavelet transform when applied to stochastic processes have been studied exclusively from the increasing-domain perspective, in which the distance between neighboring observations stays roughly constant as the number of observations increases. To understand the underlying data-generating process and to obtain good interpolations, fixed-domain asymptotics, in which the number of observations increases in a fixed region, is often more appropriate than increasing-domain asymptotics. In the fixed-domain setting, we prove that, for a general class of inhomogeneous covariance functions, with suitable choice of wavelet filters, the wavelet transform of a nonstationary process has mostly asymptotically uncorrelated components.

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