Design and properties of anti-symmetric biorthogonal wavelet filter banks with the same even length

With excellent time-frequency local and multiresolution analysis characteristic, wavelet transform is widely used in signal and image processing. A new class of biorthogonal wavelet filter banks, named anti-symmetric biorthogonal wavelet filter banks with the same even length, was constructed in this paper. The paper deduced design formulas and then described design steps detailedly. Furthermore, properties of this class of wavelet were studied, and particularly differential operator property was analyzed in detail. As an example, this paper gave filter coefficients of the anti-symmetric Bior5.5 and drew their graphs of dual wavelet functions, which proved these properties of this class of wavelet correctly.