I know group of translations in momentum space generate fourier transform. Because in fourier transform we decompose a function as a sum different frequency components
$e^{ikx} $
What group of translations on momentum space do is
$U (k) e^{ifx} = e^{i(f-k)x} $
As this k runs over all its group elements through integration we get fourier transform from a fixed fiducial vector in momentum space.
What I need to know is, Can affine transformations in position or momentum space generate continues Wavelet transform?