  Wavelet analysis has been extended to the $p$-adic line $\mathbb{Q}_p$. The
$p$-adic wavelets are complex valued functions with compact support. As in the
case of real wavelets, the construction of the basis functions is recursive,
employing scaling and translation. Consequently, wavelets form a representation
of the affine group generated by scaling and translation. In addition, $p$-adic
wavelets are eigenfunctions of a pseudo-differential operator, as a result of
which they turn out to have a larger symmetry group. The enhanced symmetry of
the $p$-adic wavelets is demonstrated.
