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Journal Articles IEEE Signal Processing Letters Year : 2002

Stochastic Discrete Scale Invariance

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Pierre Borgnat
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Patrick Flandrin
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Abstract

A definition of stochastic discrete scale invariance (DSI) is proposed and its properties studied. It is shown how the Lamperti transformation, which transforms stationarity in self-similarity, is also a means to connect processes deviating from stationarity and processes which are not exactly scale invariant: in particular we interpret DSI as the image of cyclostationarity. This theoretical result is employed to introduce a multiplicative spectral representation of DSI processes based on the Mellin transform, and preliminar remarks are given about estimation issues.
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Dates and versions

ensl-00175962 , version 1 (01-10-2007)

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  • HAL Id : ensl-00175962 , version 1

Cite

Pierre Borgnat, Patrick Flandrin, Pierre-Olivier Amblard. Stochastic Discrete Scale Invariance. IEEE Signal Processing Letters, 2002, 9 (6), pp.181-184. ⟨ensl-00175962⟩
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