A general approach to the generation of biorthogonal bases of compactly-supported wavelets
نویسندگان
چکیده
Biorthogonal bases of compactly-supported wavelets are characterized by the FIR perfect-reconstruction filterbanks to which they correspond. In this paper we develop explicit representations of all such filterbanks, allowing us to generate every possible biorthogonal compactly-supported wavelet basis. For these filterbanks, the product H(z) = H(z) e H(z) of the two lowpass filters must have N 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 H(z) with even N ; other filterbanks lead to novel biorthogonal bases.
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