Optimized Lagrange and spline-based interpolators

In many signal processing applications it is beneficial to use polynomial-based interpolation filters. Actual implementations of these filters can be performed effectively by using the Farrow structure or its modifications. In the literature, several design methods have been proposed. Two widely used methods for finding the polynomial coefficients are based on the use of the classical Lagrange and B-spline interpolations. However, the cost of this advantage is that the filter design is not very flexible since the only design parameter is the degree of the polynomials M, that is, for the given M, the polynomial coefficients are uniquely determined. In this paper, we introduce a novel design method which introduces more degrees of freedom. In the proposed approach, the piecewise-polynomial impulse response of the filter is optimized directly in the frequency domain using either minimax or least-mean-square by combining several Lagrange or B-spline interpolators of different order.