Biorthogonal Butterworth wavelets derived from discrete interpolatory splines

We present a new family of biorthogonal wavelet transforms and a related library of biorthogonal periodic symmetric waveforms. For the construction, we used the interpolatory discrete splines, which enabled us to design a library of perfect reconstruction filterbanks. These filterbanks are related t...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2001-11, Vol.49 (11), p.2682-2692
Main Authors: Averbuch, A.Z., Pevnyi, A.B., Zheludev, V.A.
Format: Article
Language:English
Subjects:
Butterworth filters
Construction
Discrete Fourier transforms
Discrete wavelet transforms
Fast Fourier transforms
Filters
Fourier transforms
Frequency domain analysis
Hoisting
Interpolation
Libraries
Polynomials
Splines
Waveforms
Wavelet packets
Wavelet transforms
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Summary:We present a new family of biorthogonal wavelet transforms and a related library of biorthogonal periodic symmetric waveforms. For the construction, we used the interpolatory 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 a linear-phase property, and the basic waveforms are symmetric. In addition, these filters yield refined frequency resolution.
ISSN:1053-587X
1941-0476
DOI:10.1109/78.960415