A frequency estimator for estimating the frequency of a digital input signal (x(k)) includes a phase detection device (2) for determining the phase (&phgr;(k)) of the input signal (x(k)), a differentiator (3) for generating the phase difference (&phgr;diff1(k)) between adjacent samples of the phase (&phgr;(k), &phgr;(k-1)) and a filter (4) for averaging the phase difference (&phgr;diff(k)) and having a trapezoidal pulse response (hM(k)). The trapezoidal pulse response (hM(k)) is generated by superimposing a first triangular pulse response with a second triangular pulse response which is offset in time with respect to the first triangular pulse response.