ON ASYMPTOTIC CONVERGENCE OF THE DUAL FILTERS ASSOCIATED WITH 2 FAMILIES OF BIORTHOGONAL WAVELETS

The asymptotic behavior of the dual filters associated with biorthogon al spline wavelet (BSW) systems and general biorthogonal Coifman wavel et (GBCW) systems are studied. As the order of the wavelet systems app roaches infinity, the magnitude responses of the dual filters in the B SW systems either diverge or converge to some nonideal frequency respo nses. However, the synthesis filters in the GBCW systems converge to a n ideal halfband low pass filter without exhibiting any Gibbs like phe nomenon, and a subclass of the analysis filters also converge to an id eal halfband lowpass filter but with a one-sided Gibbs-like behavior. The two approximations of the ideal lowpass filter by the filter assoc iated with a Daubechies orthonormal wavelet and by the synthesis filte r in a GBCW system of the same order are compared. Such a study of the asymptotic behaviors of wavelet systems provides insightful character ization of these systems and systematic assessment and global comparis on of different wavelet systems.