Oversampling invariance of wavelet frames

It is shown that for all wavelet frames that have filter banks associated with them, oversampling by a factor of N preserves the frame property with the same dual frame (oversampled by N) iff (N, M)=1. In particular, tight frames are preserved by oversampling by N, with (N, M)=1. The results are sharper for the case of filter bank (FB) wavelet frames. It is conjectured that all compactly supported wavelet frames are FB wavelet frames.<>