On asymptotic convergence of the dual filters associated with two families of biorthogonal wavelets

The asymptotic behavior of the dual filters related with biorthogonal spline wavelet (BSW) systems and general biorthogonal Coifman wavelet (GBCW) systems were analyzed. Results indicated that magnitude responses of the dual filters in BSW systems diverge or converge to frequency responses. On the other hand, synthesis filters in the GBCW systems converge to halfband lowpass filter.