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An abstract sampling theory associated to a unitary representation of acountable discrete non abelian group $G$, which is a semi-direct product ofgroups, on a separable Hilbert space is studied. A suitable expression of thedata samples and the use of a filter bank formalism allows to fix themathematical problem to be solved: the search of appropriate dual frames for$\ell^2(G)$. An example involving crystallographic groups illustrates theobtained results by using average or pointwise samples.

Semi-direct product of groups, filter banks and sampling