Construction of m-band Orthonormal Wavelets by 2N-point m-ary Interpolatory Subdivision Schemes

The aim of the paper is to construct an m-band orthonormal wavelet with some good properties.A new method to construct m-band orthonormal wavelets based on m-ary subdivision schemes is presented.First,we construct an m-band orthonormal refinable function based on an m-ary 2N-point interpolatory subdivision scheme,whose basic limit function is the autocorrelation function of the refinable function,and then construct orthonormal wavelets using the orthonormal refinable function.Moreover,the property of vanishing moments of the orthonormal wavelets is analyzed.The feasibility of the method is exposed in three examples and a new 2-band orthonormal wavelet with a tension parameter is constructed.