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Communication Dans Un Congrès Année : 2007

Galton Watson fractal signals

Résumé

Iterated Function Systems (IFS) is a relevant model to produce fractal functions, whether deterministic (with strict self-similarity) or random (self-similar up to probability distribution). The basic idea of such a construction is to start with an initial function and then compress, dilate and translate it such that by doing so over and over again, we end up with a self-similar signal. This construction relies on a construction tree which has always been deterministic in the litterature for signals. Here we introduce new fractals, called Galton Watson fractals, as fixed points of IFS with a random underlying construction tree and deterministic operators. We give a proof of the existence and uniqueness of a fixed point at the random and distribution level.
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Dates et versions

hal-00384636 , version 1 (15-05-2009)

Identifiants

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Geoffrey Decrouez, Pierre-Olivier Amblard, Jean-Marc Brossier, O. D. Jones. Galton Watson fractal signals. ICASSP 2007 - IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2007, Honolulu, Hawaii, United States. pp.III-1157 - III-1160, ⟨10.1109/ICASSP.2007.366890⟩. ⟨hal-00384636⟩
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