52. Towards a Wavelet Information Theory

This note reports a new reading for wavelets, which is based on the classical De Broglie principle.
Some kind of duality "wave-particle" behaviour can be adapted to wavelets.
The continuous basic wavelet is associated to a probability density on both time and frequency domain,
allowing to define the Shannon entropy of a wavelet. It is shown that any wavelet of the same family
has the same entropy of the mother wavelet. The entropy for a few standard wavelet families is determined.
The foundations of a wavelet information theory are completed by introducing the concept of
wavelet mutual information between a signal and an analysing wavelet.