Precise knowledge of a laser's wavelength is crucial for applications from spectroscopy to telecommunications. Here, we present a wavemeter that operates on the Talbot effect. Tone parameter extraction algorithms are used to retrieve the frequency of the periodic signal obtained in the sampled Talbot interferogram. Theoretical performance analysis based on the Cramér-Rao lower bound as well as experimental results are presented and discussed. With this scheme, we experimentally demonstrate a compact and high-precision wavemeter with below 10 pm single-shot estimation uncertainty under the 3-σ criterion around 780 nm.