98-400 Stein C.F. , Holschneider M.

On the Asymptotic Behaviour of QMFs with Single Factor Loops (321K, .eps-file (gzipped and uuencoded)) May 28, 98

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Abstract. 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.

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