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Summary: Signal Processing 81 (2001) 23632382
www.elsevier.com/locate/sigpro
Butterworth wavelet transforms derived from discrete
interpolatory splines: recursive implementation
Amir Z. Averbucha;
, Alexander B. Pevnyib
, Valery A. Zheludeva
aSchool of Mathematical Science, Department of Computer Science, Tel Aviv University, Ramat Aviv,
Tel Aviv 69978, Israel
bDepartment of Mathematics, Syktyvkar University, Syktyvkar, Russia
Received 27 November 2000; received in revised form 6 April 2001
Abstract
In the paper we present a new family of biorthogonal wavelet transforms and the related library of biorthogonal
symmetric waveforms. For the construction we used the interpolatory discrete splines which enabled us to design a
library of perfect reconstruction ˙lter banks. These ˙lter banks are related to Butterworth ˙lters. The construction
is performed in a "lifting" manner. The di erence from the conventional lifting scheme is that the transforms of a
signal are performed via recursive ˙ltering with the use of IIR ˙lters. These ˙lters have linear phase property and
the basic waveforms are symmetric. The ˙lters allow fast cascade or parallel implementation. We present explicit
formulas for construction of wavelets with arbitrary number of vanishing moments. In addition, these ˙lters yield
perfect frequency resolution. The proposed scheme is based on interpolation and, as such, it involves only samples
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