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Wavelet-based representations for the 1/f family of fractal processes

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Wornell, G.W. 
Res. Lab. of Electron., MIT, Cabridge, MA 

This paper appears in: Proceedings of the IEEE
Issue Date: Oct 1993
Volume: 81 Issue: 10
On page(s): 1428 - 1450
ISSN: 0018-9219
Cited by: 44
INSPEC Accession Number: 4583150
Digital Object Identifier: 10.1109/5.241506
Date of Current Version: 06 August 2002

Abstract

It is demonstrated that 1/f fractal processes are, in a broad sense, optimally represented in terms of orthonormal wavelet bases. Specifically, via a useful frequency-domain characterization for 1/f processes, the wavelet expansion's role as a Karhunen-Loeve-type expansion for 1/f processes is developed. As an illustration of potential, it is shown that wavelet-based representations naturally lead to highly efficient solutions to some fundamental detection and estimation problems involving 1/f processes

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