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 {ψa,b(t)}a6=0 has the same Shannon entropy of its mother wavelet. Finally, the Shannon entropy for a few standard wavelet families is determined. 1