Biorthogonal Butterworth wavelets

We present a new family of biorthogonal wavelet transforms and a related library of biorthogonal symmetric wavelets. For the construction we use the interpolatory discrete splines which enable us to design perfect reconstruction filter banks related to the Butterworth filters. The construction is performed in a "lifting" manner. The proposed scheme is based on interpolation and, as such, it involves only samples of signals and it does not require any use of quadrature formulas. These filters have linear phase property. The filters yield perfect frequency resolution.