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Signal Processing ] (]]]]) ]]]]]] Wavelet-based synthesis of the Rosenblatt process

Summary: Signal Processing ] (]]]]) ]]]­]]]
Wavelet-based synthesis of the Rosenblatt process
Patrice Abrya,Ã, Vladas Pipirasb
CNRS UMR 5672, Ecole Normale Supe´rieure de Lyon, Laboratoire de Physique, 69364 Lyon Cedex 07, France
Department of Statistics and Operations Research, Smith Building, CB #3260, University of North Carolina at Chapel Hill,
Chapel Hill, NC 27599, USA
Received 8 March 2005; accepted 26 October 2005
Based on a wavelet-type expansion of the Rosenblatt process, we introduce and examine two different practical ways to
simulate the Rosenblatt process. The synthesis procedures proposed here are obtained by either truncating the series of the
approximation term or using the approximation coefficients in the wavelet-type expansion of the Rosenblatt process. Both
benefit from the low computational cost usually associated with the discrete wavelet transform. We show that the number
of zero moments of a related orthogonal multiresolution analysis plays an important role. We study in detail the wavelet-
based simulation in terms of uniform convergence. We also discuss at length the importance of the choices of the initial and
final resolutions, the specific case of the simulation on the integer grid as well as the usefulness of the wavelet-based
simulation. Matlab routines implementing these synthesis procedures as well as their analysis are available upon request.
r 2005 Elsevier B.V. All rights reserved.
Keywords: The Rosenblatt process; Long-range dependence; FARIMA sequence; Wavelet-type expansion; Low and high-pass filters; Zero


Source: Abry, Patrice - Laboratoire de Physique, Ecole Normale Supérieure de Lyon


Collections: Engineering