Implementation of Farrow structure based interpolators with subfilters of odd length

Interpolation filters are used to interpolate new sample values at arbitrary points between existing discrete-time samples. An interesting class of such filters is polynomial-based interpolation filter. These filters can be efficiently implemented using the Farrow structure and its modifications. Traditionally, the polynomial based interpolation filters have been implemented by using Farrow structure with finite impulse response (FIR) subfilters of even length. This paper presents the modification of the Farrow structure, which can have FIR subfilters of odd length. Applying the proposed modification of this paper will result in a natural implementation form for even order Lagrange and spline based interpolators. The obtained results provides more freedom in designing Farrow structure based filters, as structures with odd and even length FIR subfilters may be equally applied. These results are extended to a modified Farrow structure case as well, in which the number of multipliers is nearly halved.