A Simplified Method to Get the Optimal Coefficients of Lagrange-Constrained Polynomial Interpolators

This paper presents a simplified algorithm to get the optimal coefficients of Lagrange-constrained polynomial interpolators. The Lagrange-constrained interpolators are widely used in communication systems. They are used to compensate timing offsets in time domain and to recover carrier frequency in frequency domain. There are methods to get the optimal coefficients of Lagrange-constrained polynomial interpolators. However, all these methods are very complicated. The proposed method exploits the correlations between the interpolators' optimal coefficients caused by constraints and the symmetry characteristic. The number of the undefined coefficients, including the optimal coefficients, is efficiently reduced without any degradation of the interpolators' performance.