**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.