This paper describes the main characteristics of a new microprocessor-implemented2400-bitls 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.At the relatively low data rate of 2400 bits/s, line distortions and impairments are usually not severe enough to require the implementation of sophisticated signal processing techniques, which explains why most 2400-bit/s modems are only equipped with compromise, possibly manually selectable, equalizers.