Fast initial training of a voiceband data-modem receiver which employs an equalizer with fractionl-Tspaced coefficients is presented. The modem receiver performs rapid gain acquisition, and monitors the equalizer delay line for the presence of a periodic training signal whose period is equal to the length of the equalizer delay line. Testing for periodicity is combined with estimating carrier-frequency offset. Once a full period of the training signal has been obtained, the equalizer coefficients are computed by spectral division, and coefficient centering is performed. The receiver then proceeds in a reference-directed mode until the end of the training signal is detected. In the paper, algorithms for rapid gain acquisition and the detection of a cyclic training signal in the presence of noise and carrier-frequency offset are presented. Cyclic training of an equalizer with fractional-Tspaced coefficients is derived. It is shown that the equalizer coefficients can be computed efficiently by spectral division. Coefficient centering, carrier-phase and symbol synchronization, reference-directed training, and the transition to data mode are described. Finally, measurement results for an experimental 2400 baud modem using an equalizer with 64T/2-spaced coefficients are given. The modem achieves a startup time of 20 ms on a Bell 3002 unconditioned leased line.