Estimation of the number of polynomial segments and the polynomial order of prolonged Farrow structure

Polynomial-based filters has been popular in many DSP application whenever there is a need for signal interpolation or programmability. Actual implementations of these filters can be performed effectively by using the Farrow structure or its modifications. Among these modifications, a very interesting is a prolonged version of the Farrow structure. The prolonged Farrow structure is derived from original by extending its impulse response by an integer factor. The prolonged Farrow structure is especially convenient for the design of narrow band filters. The basic two design parameters are the number of polynomial-segments defining the finite length of the underlying continuous-time filter impulse response and the order of polynomials in each polynomial segment. This contribution presents estimation formulae for the length and the polynomial order of prolonged Farrow structure.