Abstract
We study the construction of Gabor frames and wavelet frames for Weyl–Heisenberg group and extended affine group by using contraction between the affine group and the Weyl–Heisenberg group due to Subag, Baruch, Birman and Mann. Firstly, we give construction of Gabor frames with several generators from a unitary irreducible representation associated with the Weyl–Heisenberg group. Wavelet frames with several generators associated with an extended affine group have been obtained. A relation between frames for Weyl–Heisenberg group and extended affine group is also discussed. Finally, we show that frames of Gabor and wavelet structure are stable under small perturbations.
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