Generalization and Coefficients Optimization of the Newton Structure

The Newton structure is a very efficient implementation of a variable fractional delay filter performing Lagrange interpolation. In this paper, we study the generalization of this structure by developing the closed form expressions of the generalized structure. Through this, any Farrow structure can be replaced by the Newton structure that is more efficient in terms of complexity. Moreover, the closed form expression of the frequency response of the generalized Newton structure is developed. This expression enables the application of filter optimization methods to build customized Newton structures. We demonstrate how this makes possible the design of optimized Newton structures that offer a reduction in complexity by half compared to their Farrow counterparts, while keeping a similar filtering performance.