Trigonometric polynomial interpolation for timing recovery

In an all-digital timing-adjustment system for digital modems, interpolation can be employed to recover samples that are synchronous with the data symbols. In this paper, a novel interpolation method is described for such systems. Instead of approximating a continuous-time signal with a conventional (algebraic) polynomial and computing the synchronized samples using a Farrow structure, a trigonometric polynomial is employed. It is demonstrated that this approach produces a particularly simple implementation structure, reduces computational delay and, for practical signals, can improve the interpolation performance. Moreover, to recover a synchronized sample from existing samples, given a timing offset, it is shown that the method can be optimized such that a recovered sample's interpolation error is minimized for that specific timing offset value. The input signal's spectrum is also taken into account. Simulation results indicate that the method can achieve the best performance among all state-of-the-art methods tested. In addition, the optimal interpolator can be implemented without increased hardware requirements.