Construction of m-ary Symmetric Interpolatory Subdivision Scheme by m-ary Orthonormal Refinable Function

A new method to construct mary (for any) symmetric interpolatory subdivision scheme for curves design based on the orthonormal refinable function is introduced. In this paper, we study the properties of the autocorrelation function of a m-band compactly supported orthonormal refinable function, then we construct a m-ary interpolatory subdivision scheme based on these properties. The family of the subdivision schemes which we construct is convergent naturally. The feasibility of our method is exposed in two examples.