  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.
