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Decorrelation Property of Discrete Wavelet Transform Under Fixed-Domain Asymptotics

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2 Author(s)
Xiaohui Chang ; Dept. of Stat., Univ. of Chicago, Chicago, IL, USA ; Stein, M.L.

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.

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Information Theory, IEEE Transactions on  (Volume:59 ,  Issue: 12 )