Convergence of the Newton Structure Transfer Function to the Ideal Fractional Delay Filter

This letter presents a rigorous demonstration of the convergence of the Newton fractional-delay filter to the ideal fractional delay filter. The Newton structure is a very efficient implementation of Lagrange interpolation using a variable fractional delay filter structure. Through the developed demonstration, a new approach is proposed to define the ideal fractional delay filter as the limit of any digital filter implementing on Lagrange interpolation. This letter also proves that the Z-transform expression of the ideal fractional delay has a fully defined frequency response on the unit circle.