61. Shannon and Renyi Entropy of Wavelets

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 that any wavelet of the same family has the same
Shannon entropy of its mother wavelet. Finally, the Shannon entropy for a few standard wavelet families is determined.