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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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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cited_by cdi_FETCH-LOGICAL-c370t-84c21c987b5d8a7e7c8909f6145ba7cc0cc35d4aeecce291b3fa5d73f2f5f32d3
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container_end_page 2692
container_issue 11
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container_title IEEE transactions on signal processing
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creator Averbuch, A.Z.
Pevnyi, A.B.
Zheludev, V.A.
description 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.
doi_str_mv 10.1109/78.960415
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source IEEE Electronic Library (IEL) Journals
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
title Biorthogonal Butterworth wavelets derived from discrete interpolatory splines
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