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We study the relationship between the (1+1)-affine Galilei group and fourgroups of interest in signal analysis and image processing, viz., the waveletor the affine group of the line, the Weyl-Heisenberg, the shearlet and theStockwell groups. We show how all these groups can be obtained either directlyas subgroups, or as subgroups of central extensions of the affine Galileigroup. We also study this at the level of unitary representations of the groupson Hilbert spaces.

All the Groups of Signal Analysis from the (1+1)-affine Galilei Group