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Decorrelation Property of Discrete Wavelet Transform Under Fixed-Domain Asymptotics | IEEE Journals & Magazine | IEEE Xplore

Decorrelation Property of Discrete Wavelet Transform Under Fixed-Domain Asymptotics


Abstract:

Theoretical aspects of the decorrelation property of the discrete wavelet transform when applied to stochastic processes have been studied exclusively from the increasing...Show More

Abstract:

Theoretical aspects of the decorrelation property of 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.
Published in: IEEE Transactions on Information Theory ( Volume: 59, Issue: 12, December 2013)
Page(s): 8001 - 8013
Date of Publication: 25 October 2013

ISSN Information:


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