Sampling Associated with a Unitary Representation of a Semi-Direct Product of Groups: A Filter Bank Approach Articles uri icon

publication date

  • April 2019

issue

  • 4

volume

  • 11

International Standard Serial Number (ISSN)

  • 2073-8994

abstract

  • An abstract sampling theory associated with a unitary representation of a countable discrete non abelian group G, which is a semi-direct product of groups, on a separable Hilbert space is studied. A suitable expression of the data samples, the use of a filter bank formalism and the corresponding frame analysis allow for fixing the mathematical problem to be solved: the search of appropriate dual frames for l2(G). An example involving crystallographic groups illustrates the obtained results by using either average or pointwise samples.

keywords

  • semi-direct product of groups; unitary representation of a group; LCA groups; dual frames; sampling expansions