Does anybody know an example of a normalized tight frame (wavelet frame) that is not an orthonormal frame of $L^2( \mathbb{R})$?

So in other words $\{\psi_{j,k}(x):=2^{j/2}\,\psi(2^j\,x-k)\}_{j,k \in \mathbb{Z}}$ is supposed to be a frame satisfying $||f||_2 = \sum_{j,k} |\langle f , \psi_{j,k} \rangle|^2 , $ but the $\psi_{j,k}$ shall not form an ONB.

I am looking for such an example in the literature, but so far I did not find one.

Does anybody know an example of a normalized tight frame (wavelet frame) that is not an orthonormal frame of $L^2( \mathbb{R})$?

So in other words $\{\psi_{j,k}(x):=2^{j/2}\,\psi(2^j\,x-k)\}_{j,k \in \mathbb{Z}}$ is supposed to be a frame satisfying $||f||^2_2 = \sum_{j,k} |\langle f , \psi_{j,k} \rangle|^2 , $ but the $\psi_{j,k}$ shall not form an ONB.

I am looking for such an example in the literature, but so far I did not find one.