A method of signal sample interpolation utilizing a second order curve comprising the steps of utilizing a linear interpolator to select a mid-point between respective input samples, thereby eliminating phase error and spatial variation, utilizing the interpolated points as reference points for a quadratic interpolation wherein the space between the reference points is one half the distance between respective signal sample points, and thirdly combining the operations of linear interpolation and quadratic interpolation for simultaneous execution. More particularly, the quadratic interpolation is reformed based on the output of the linear interpolation.