A modem for use in a simulcast paging system includes a modulator (26) and a demodulator (30), both of which produce very low jitter, enabling the modem to be used at data rates well in excess of 1,200 baud. Both the modulator and the demodulator are implemented in software using a digital signal processor (DSP) (66). The modulator initially samples a non-return-to-zero (NRZ) input at a sample rate of 19.2 KHz, interpolates transitions between logic levels, and produces a frequency shift keyed (FSK) modulated signal at a center frequency different than that used for transmitting the modulated signal. Using an interpolation timer that responds to changes in logic level on the input, the modulator changes the frequency of the FSK modulated signal at the appropriate time with much greater accuracy than would be possible without interpolation. The FSK modulated signal is filtered to substantially attenuate frequencies outside a 3 KHz bandwidth, producing a filtered signal. By frequency shifting the filtered signal (either up or down) to a center frequency of approximately 1,700 Hz, interference between positive and negative frequencies is substantially eliminated. A digital-to-analog converter (DAC) (74) produces an analog FSK modulated signal. At a receiving modem (29), the demodulator digitizes the FSK modulated signal at a 19.2 KHz sample rate and shifts the digitized modulated signal to a center frequency of 0 Hz, producing a complex baseband comprising in-phase (real) and quadrature (imaginary) components. The DSP determines the instantaneous phase of the complex baseband signal, and from the time derivative of the instantaneous phase, determines its frequency. The instantaneous frequency is interpolated at eight times the major sample rate, producing an interpolated frequency signal so that changes in the sign of the interpolated frequency can be used to determine the logic level and zero crossing of the demodulated signal with greater resolution, substantially reducing jitter. Correlation of the demodulated signal at the data rate further reduces jitter.