From the development of the problem, developments the super-wavelets in theory mathematics and their achievements are discussed. The characters of extending a normalized tight frame wavelet to a super-wavelet and the construction methods of super-wavelets by using affine structure are introduced. Lastly, a few open problems are listed and some new possible directions of research one pointed out. The super-wavelet is a signal analysis method based on wavelet analysis. There are some important results on extending a normalized tight frame wavelet to a super-wavelet, but there are some open problems on finding a sufficient and necessary condition for a normalized tight frame wavelet to be extended to a super-wavelet and the important aspects of the MRA super-wavelets also open.

super-wavelet; normalized tight frame wavelet; affine structure