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.