  Precise knowledge of a laser's wavelength is crucial for applications from
spectroscopy to telecommunications. Here we present a wavemeter which 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 Cram\'er-Rao lower
bound (CRLB) 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-$\sigma$ criterion around 780 nm.
