A biorthogonal wavelet
is a wavelet
where the associated wavelet transform
but not necessarily orthogonal
Designing biorthogonal wavelets allows more degrees of freedoms than orthogonal wavelets
One additional degree of freedom is the possibility to construct symmetric wavelet functions.
In the biorthogonal case, there are two scaling functions , which may generate different multiresolution analyses, and accordingly two different wavelet functions . So the numbers M, N of coefficients in the scaling sequences may differ. The scaling sequences must satisfy the following biorthogonality condition
Then the wavelet sequences can be determined as