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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 impulse response filters of a Hilbert-pair of wavelets serving as real and imaginary part of a complex wavelet. Unfortunately it is not possible to construct wavelets which are both finitely supported and analytic. The wavelet filters constructed using the common-factor approach are then approximately analytic. Thus, it is of interest to control their analyticity. The purpose of this paper is to first provide precise and explicit expressions as well as easily exploitable bounds for quantifying the analytic approximation of this complex wavelet. Then, we prove the existence of such filters enjoying the classical perfect reconstruction conditions, with arbitrarily many vanishing moments.
Cited literature [25 references]
https://hal.univ-grenoble-alpes.fr/hal-01613583
Contributor : Sophie Achard <>
Submitted on : Tuesday, July 23, 2019 - 12:38:55 AM
Last modification on : Tuesday, March 2, 2021 - 5:12:06 PM
Contributor : Sophie Achard <>
Submitted on : Tuesday, July 23, 2019 - 12:38:55 AM
Last modification on : Tuesday, March 2, 2021 - 5:12:06 PM
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