Asymptotic decorrelation of between-scale wavelet coefficients of generalized fractional process

Abstract

Recent interest on the wavelet transform of digital random signals with long-memory is significantly due to the approximate decorrelation of their wavelet coefficients, which simplifies system identification and estimation. In this paper, we show that for a fairly general model of long-memory across-scale autocovariances of wavelet coefficients converge rapidly to zero, and we determine the rate of converge. The result provides useful groundwork for wavelet-based processing of long-memory random signals.