There are several design properties for the construction of a wavelet basis that one would want to be fulfilled.

- symmetry: If the wavelets are not symmetric, then the wavelet transform of the mirror of an image is not the mirror of the wavelet transform.
- smoothness: This property is determined by the number of vanishing moments. Recall that the primal vanishing moments determine the smoothness of the reconstruction. The dual vanishing moments determine the convergence rate of the multiresolution projections and are necessary for detecting singularities.
- orthogonality: This property can be too restrictive at times. Thus the need for biorthgonal wavelet systems.
- compact support: This property is a function of the filter length.