This paper reports a new reading for wavelets, which is based on the classical ’De Broglie’ principle. The waveparticle duality principle is adapted to wavelets. Every continuous basic wavelet is associated with a proper probability density, allowing defining the Shannon entropy of a wavelet. Further entropy definitions are considered, such as Jumarie or Renyi entropy of wavelets. We proved tha...

The Tsallis entropy given for a positive parameter α can be considered as a generalization of the classical Shannon entropy. For the latter, corresponding to α = 1, there exist many axiomatic characterizations. One of them based on the well-known Khinchin-Shannon axioms has been simplified several times and adapted to Tsallis entropy, where the axiom of (generalized) Shannon additivity is playi...

Entropies. Several notions of entropies have been defined along the twentieth century. The role of an entropy is to quantify the uncertainty one has about the state of a – physical as well as mathematical – system, whose states are modeled as points of a mathematical space. The expression information content is also used in place of entropy, as uncertainty can be thought as lack of information....