This paper describes the main characteristics of a new microprocessor-implemented 2400-bit/s data modem, the IBM 3863. In addition to the execution of signal processing tasks, the microprocessor provides a variety of other significant functions such as diagnostics and aids in network problem determination. The lack of hardware multiplication capability imposes certain constraints in the design of the signal processing algorithms. The analytical approach and computational techniques, based on the processing of signals in polar coordinates, which are used to circumvent these constraints, are described. It is shown in particular that timing phase control, carrier recovery, and adaptive equalization can be achieved at the receiver by processing only the phase of the sampled signal. Additionally, experimental results are presented which demonstrate the superiority of this design over conventional coherent demodulators.