Optimal interpolator using a trigonometric polynomial

All-digital approaches for the adjustment of timing offset in digital modems have attracted increasing attention. We recently announced a novel interpolation method which, instead of approximating the continuous-time signal with a conventional polynomial and computing the synchronized samples using a Farrow structure, uses a trigonometric polynomial. Simulation results indicate that improved performance, reduced computational delay and, in most cases, simplified hardware can be achieved. To recover a synchronized sample from existing samples, given a timing offset, we show here that we can optimize this method such that the interpolation error in the recovered sample is minimized for that specific timing offset value. Using this optimization technique, the overall interpolation error is reduced. As for the implementation, the optimal interpolator does not require additional hardware as compared to our original method.