For rapidly detecting a periodic training signal in a modem receiver, delay line storage (21) is provided for a signal section which is equal to one training signal period (q.multidot.M samples) plus an additional adjacent window (q.multidot.W samples). Thus, the stored signal section includes two windows (17', 19) which are offset by one training signal period and which are similar if a training signal is present. In evaluation means (41) connected to the two windows (17', 19), two auxiliary signals (z.sub.1, z.sub.2) are generated (61, 65) which represent the signal energy and the correlation, respectively, of the samples in the two windows. From the auxiliary signals, a dissimilarity metric (z.sub.3) is derived (69) and is compared (73) to a given threshold for generating an indicator signal (CYC) which becomes active when a training signal is present, i.e. when the two window contents are similar and the metric (z.sub.3) falls below the threshold. A carrier frequency offset estimate (.DELTA..sub.f) is also derived from the second auxiliary signal (z.sub.2).