**:**In this paper we introduce different algorithm for reconstruction of a one dimensional function from its zero crossings. However, none of them is stable and computable in real time. An algorithm for computing the cubic spline interpolation coefficients for polynomials is presented in this paper. The matrix equation involved is solved analytically so that numerical inversion of the coefficient matrix is not required. For

*f*(t) = , a set of constants along with the degree of polynomial m are used to compute the coefficients so that they satisfy the Interpolation constraints but not necessarily the derivative constraints. Then, another matrix equation is solved analytically to take care of the derivative constraints. The results are combined linearly to obtain the unique solution of the original matrix equation. This algorithm is tested and verified numerically for various examples.