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

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This paper appears in:
Proceedings of the IEEE
Date of Publication: Oct 1993
Author(s): Wornell, G.W.
Res. Lab. of Electron., MIT, Cabridge, MA
Volume: 81 , Issue: 10
Page(s): 1428 - 1450
Product Type: Journals & Magazines

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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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