A general approach to the generation of biorthogonal bases of compactly-supported wavelets

Biorthogonal bases of compactly-supported wavelets are characterized by the FIR perfect-reconstruction filterbanks to which they correspond. We develop explicit representations of all such filterbanks, allowing us to generate every possible biorthogonal compactly-supported wavelet basis. For these filterbanks, the product /spl Hscr/(z)=H(z)H/spl tilde/(z) of the two lowpass filters must have N/spl ges/2 zeros at z=-1. There are N+1 minimal-length filterbanks for each N. The filterbanks associated with standard orthogonal and symmetric biorthogonal wavelet bases are found as a special case by using appropriate factorizations of symmetric /spl Hscr/(z) with even N; other filterbanks lead to novel biorthogonal bases.