Summary: 2682 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 49, NO. 11, NOVEMBER 2001
Biorthogonal Butterworth Wavelets Derived from
Discrete Interpolatory Splines
Amir Z. Averbuch, Alexander B. Pevnyi, and Valery A. Zheludev
Abstract--In the paper, we present a new family of biorthog-
onal wavelet transforms and a related library of biorthogonal pe-
riodic symmetric waveforms. For the construction, we used the in-
terpolatory discrete splines, which enabled us to design a library
of perfect reconstruction filterbanks. These filterbanks are related
to Butterworth filters. The construction is performed in a "lifting"
manner. The difference from the conventional lifting scheme is that
all the transforms are implemented in the frequency domain with
the use of the fast Fourier transform (FFT). Two ways to choose
the control filters are suggested. 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, and the basic waveforms are symmetric. In
addition, these filters yield refined frequency resolution.
Index Terms--Biorthogonal wavelets, Butterworth filters, dis-
crete splines, lifting scheme.