Optimal Farrow coefficients for symbol timing recovery

The Farrow structure provides an efficient way to implement interpolation filters. Such filters are often required in digital modems to allow symbol timing recovery. A method for generating Farrow filter coefficients that minimize the mean square error (MSE) at the symbol decision instants is presented. Minimizing the MSE at the symbol decision instants is nearly equivalent to minimizing the symbol error rate (SER) but is more mathematically convenient. The MSE at times other than the symbol decision instants does not affect the SER and is not considered in the optimization. Example coefficients are tabulated and performance is illustrated using SER results generated by computer simulation.