Abstract:This paper studies the parameterized respresentations of symmetrical interpolating scaling functions and their duals.Based on this,the optimal design method and corresponding minimax algorithm of the regularity of a novel type of interplating wavelet systems,biorthogonal interpolating wavelet system with compact supported dauls are proposed.The optimal results show that the approximation power of the system to smooth signals is markedly improved. The regularity of the duals enhances,and the magnitude responses of the dual filters are optimized.