The Hausdorff dimension of very weak self-similar fractals described by the Haar wavelet system

We observe that most signals can be described as Riesz products in the Haar wavelet system and a wide class of these products are fractals with a very weak self-similarity. For this class we show the relation of the Hausdorff dimension and the entropy of the corresponding process. Moreover we give a formula for experimental estimates of the entropy of discrete chaotic signals.