Asymmetry and self-similarity in the wavelet spectrum
Camilo Rodrigues Neto, Reinaldo Roberto Rosa, Fernando Manuel Ramos, Ademilson Zanandrea · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1999
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.