New results on approximate Hilbert pairs of wavelet filters with common factors

Abstract : In this paper, we consider the design of wavelet filters based on the Thiran common-factor approach proposed in Selesnick [2001]. This approach aims at building finite impulseresponse filters of a Hilbert-pair of wavelets serving as real and imaginary part of a complexwavelet. Unfortunately it is not possible to construct wavelets which are both finitelysupported and analytic. The wavelet filters constructed using the common-factor approachare then approximately analytic. Thus, it is of interest to control their analyticity. Thepurpose of this paper is to first provide precise and explicit expressions as well as easilyexploitable bounds for quantifying the analytic approximation of this complex wavelet.Then, we prove the existence of such filters enjoying the classical perfect reconstructionconditions, with arbitrarily many vanishing moments.
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Contributeur : Sophie Achard <>
Soumis le : mercredi 25 octobre 2017 - 07:37:12
Dernière modification le : mardi 12 mars 2019 - 11:18:04
Document(s) archivé(s) le : vendredi 26 janvier 2018 - 12:38:09


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  • HAL Id : hal-01613583, version 1
  • ARXIV : 1710.09095


Sophie Achard, Irène Gannaz, Marianne Clausel, François Roueff. New results on approximate Hilbert pairs of wavelet filters with common factors. 2017. 〈hal-01613583〉



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