Structures for Interpolation, Decimation, and Nonuniform Sampling Based on Newton’s Interpolation Formula

The variable fractional-delay (FD) filter structure by Tassart and Depalle performs Lagrange interpolation in an efficient way. We point out that this structure directly corresponds to Newton’s interpolation (backward difference) formula, hence we prefer to refer to it as the Newton FD filter. This structure does not function correctly when the fractional delay is made time-variant, e.g., in sample rate conversion. We present a simple modification that enables time-variant usage such as fractional sample rate conversion and nonuniform resampling. We refer to the new structure as the Newton (interpolator) structure. Almost all advantages of the Newton FD structure are preserved. Furthermore, we suggest that by transposing the Newton interpolator we obtain the transposed Newton structure which can be used in decimation as well as reconstruction of nonuniformly sampled signals, analogously to the transposed Farrow structure. The presented structures are a competitive alternative for the Farrow structure family when low complexity and flexibility are required.