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.

The SP16 processor executes typical signal-processing tasks efficiently by overlapping in each processor cycle four functions: instruction prefetching, data-memory access and transfer of one data word over a single data bus, ALU operation, and multiplication. Despite SP16 being a one-address machine with a single data bus, it can perform filter operations with a multiplication and ALU operation in every processor cycle.

In adaptive equalization, the coefficients of a transversal filter are automatically adjusted according to a minimum mean-square error criterion. The convolution for the filter process and the cross-correlation in the coefficient-adjustment algorithm require a large number of arithmetic operations. This paper describes an equalizer for complex signals in which filtering and coefficient adjustment are performed in the frequency domain employing Winograd's Fourier transform algorithms. Compared to the time-domain implementation, the number of multiplications is reduced by typically a factor five without increasing the number of additions. A fast initialization algorithm will be presented. In contrast to earlier work, the convergence behavior will be shown for random data signals transmitted over realistic telephone channels.