Farrow Interpolation

Farrow interpolation is a computationally efficient method for implementing a variable Fractional Delay Filter. The interpolated output is expressed as a polynomial in the fractional delay $\mu \in [0,1)$:

$$y[\mu ]=\sum _{m=0}^M{v}_m\cdot {\mu }^m$$

• where each $v_m={\sum }_n{c}_m[n]\cdot x[k-n]$ is the output of a fixed FIR subfilter with precomputed coefficients $c_m[n]$.
• The subfilter outputs $v_m$ are combined at runtime using Horner’s Method, making the cost of varying $\mu$ very low.
• Lagrange Polynomial Interpolation is a special case of Farrow interpolation.