A modulator that modulates and encodes data using data symbols, interspersed with pilot symbols, for transmission to another modem, and a demodulator that decodes data symbols of a signal received from another modem. In the demodulator, a received signal is sampled at four times the symbol rate. The sampled signal is converted to quadrature signals and low-pass filtered to produce a complex baseband signal. Data symbols in the complex baseband signal are sampled in synchronization with the start of each symbol based on the pilot symbols that are interspersed in the signal. By processing the pilot symbols, full modem synchronization is maintained down to a very low signal-to-noise ratio, through noise bursts, or even when the data symbols representing data are replaced by predefined sequences of data symbols that convey the dots and dashes of Morse code identifying the station transmitting the modulated signal. The continued presence of pilot symbols interspersed with the sequences of data symbols conveying Morse code prevents loss of synchronization between the transmitting station and the receiving station. The pilot symbols are also used to update equalizer tap coefficients in an equalizer of the demodulator, thereby minimizing errors in the output data caused by channel fading, noise, and other effects. In addition, the sequence of pilot symbols is used to delimit data frames, so that bit synchronization and frame synchronization in the data are not required.