The Poincar´e wavelet transform: Implementation and interpretation

Numerical implementation and examples of calculation of the Poincaré wavelet transform for model space-time signals are presented. This transform is a coefficient in the decomposition of solutions of the wave equation in terms of elementary localized solutions found in [1]. Elementary localized solutions are shifted and scaled versions of some chosen solution in a given reference frame, as well as in frames moving with respect to given the one with different constant speeds. We discuss what information about the wave field can be extracted from the Poincaré wavelet transform.