A discrete trigonometric interpolation method

Interpolation theory is a necessary and crucial tools for many applied engineering sciences. In this paper, we propose a new kind of 2-period interpolation of functions with period 2 at the nodes x k = x k;n = k=n; (k = 0; 1; ; 2n ? 1). We nd out the necessary and suucient conditions for regularity of this new interpolation problem. Moreover, a closed form expression for the interpolation polynomial is given. Our interpolation is of more practical signiicance. Our results provide the theoretical basis for using our interpolation in practical problems.