Asymptotic convergence of biorthogonal wavelet filters

Abstract

We study the asymptotic behavior of the dual filters associated with biorthogonal spline wavelets (BSWs) and general biorthogonal Coifman wavelets (GBCWs). As the order of wavelet systems approaches infinity the BSW filters either diverge or converge to some non-ideal filters, the GBCW synthesis filters converge to an ideal halfband lowpass (HBLP) filter without exhibiting any Gibbs-like phenomenon, and a subclass of the analysis filters also converge to an ideal HBLP filter but with a one-sided Gibbs-like behavior. The two approximations of the ideal HBLP filter by Daubechies orthonormal wavelet filters and by the GBCW synthesis filters are also compared.