Biorthogonal butterworth wavelets derived from discrete interpolatory splines

Amir Z. Averbuch*, Alexander B. Pevnyi, Valery A. Zheludev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In the paper, 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 linear-phase property, and the basic waveforms are symmetric. In addition, these filters yield refined frequency resolution.

Original languageEnglish
Pages (from-to)2682-2692
Number of pages11
JournalIEEE Transactions on Signal Processing
Volume49
Issue number11
DOIs
StatePublished - Nov 2001

Funding

FundersFunder number
Israel Science Foundation258/99-1

    Keywords

    • Biorthogonal wavelets
    • Butterworth filters
    • Discrete splines
    • Lifting scheme

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