Efficient algorithms and structures for fractional delay filtering based on lagrange interpolation

Fractional delay (FD) filtering is a technique for the calculation of arbitrarily delayed signal values from band-limited discrete-time sequences. Lagrange interpolation is a widely used method for FD interpolation. It is especially suited for applications where the delay value changes frequently, because the filter coefficients can be calculated by means of explicit formulas. Because of the widespread application of Lagrange interpolation, efficient algorithms and structures for the calculation of the filter coefficients and for the filtering are of great importance. A number of existing algorithms for Lagrange interpolation are surveyed and a concise analysis of the computational effort is provided. Based on existing methods, a novel structure for Lagrange interpolation is derived, which is very efficient in terms of computational resources, scalable, and well suited to parallel implementation in hardware or software.