A frequency-domain approach to polynomial-based interpolation and the Farrow structure

Interpolation filters are used to interpolate new sample values at arbitrary points between the existing discrete-time samples. One interesting class of these filters is the polynomial-based interpolation filters which can be efficiently implemented using the Farrow structure. This discrete-time filter structure has a time-varying impulse response. Therefore, it is usually modeled by a simple hybrid analog/digital (A/D) system which is based on the reconstruction of the continuous-time signal. In this work, an interesting frequency-domain relationship between the Farrow structure and the hybrid A/D model is derived. This result can be utilized to develop efficient design algorithms for polynomial-based interpolation filters.