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

Authors:
Alex Gonzaga;Akira Kawanaka
Affiliations:
Department of Physical Sciences and Mathematics, University of the Philippines, Padre Faura St., Manila 1000, Philippines and Department of Electrical and Electronics Engineering, Sophia Universit ...;Department of Electrical and Electronics Engineering, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan
Venue:
Digital Signal Processing
Year:
2006

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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.