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   -> Volume 7, Issue 6

Preprint: On the Asymptotic Behaviour of a Class of QMFs
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Carl-Fredrik Stein (

PostPosted: Fri May 29, 1998 8:28 am    
Subject: Preprint: On the Asymptotic Behaviour of a Class of QMFs
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#3 Preprint: On the Asymptotic Behaviour of a Class of QMFs

Title: On the Asymptotic Behaviour of QMFs with Single Factor Loops

Authors: Carl Fredrik Stein
Matthias Holschneider


Recently a parametrization of biorthogonal QMF by means of elementary
loops in SL(2) has been proposed generalizing the factorization of
orthogonal QMF through loops in U(2). These factorizations can easily
be realized by some network of elementary propagators. In this paper
we discuss the asymptotic shape of the QMFs that are obtained by
iterating one elementary factor in this parametrization. It turns out
that in the case of orthogonal QMFs the shape is asymptotically
described by some Airy function as the supports of the filters
increase. In the bi-orthogonal case instead we obtain asymptotically a
quadratic chirp. Similar results are to be expected when more factors
are involved.

Keywords: QMF; factor loops; asymptotic analysis; Airy function;
quadratic chirp

The Preprint is currently available at
Preprint no. 1998:20
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