26 October 1999 Asymmetry and self-similarity in the wavelet spectrum
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Abstract
One of the most remarkable properties of wavelet transform is its ability to separate data into different scale contents. For data that show self-similar characteristics in every scale, like fractal landscape, the wavelet spectrum also shows self-similarity. Nevertheless, the situation is not so clear for time dependent data, like seismic geology, solar flares, among others systems that are known to contain self-organized criticality. It is not obvious that these properties will be present in the wavelet spectrum in the form of self-similarity. In this work, we apply two gradient field computational operators R2 yields R, the Complex Entropic Form and the Asymmetric Amplitude Fragmentation, as a mean to differentiate self-similarity from different sources.
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Camilo Rodrigues Neto, Reinaldo Roberto Rosa, Fernando M. Ramos, Ademilson Zanandrea, "Asymmetry and self-similarity in the wavelet spectrum", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); doi: 10.1117/12.366849; https://doi.org/10.1117/12.366849
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