The invention relates to methods for receiving and transmitting discrete (digital) data signals and can be used in communication, location, telemetry, telephony and other fields involving various types of data processing. The technical result is that of reducing the energy and spectral band of data signals while keeping them distinct from all known signals, save for those proposed in the prototype, which consists in fundamentally and significantly exceeding the Shannon limit. This result is achieved on the transmit side in that each data symbol is mapped to a short sequence of periodic disturbances (wave train) of an arbitrary physical medium, which sequence can be transmitted across a transmission medium directly or used as a modulating signal. Transmission takes place in the frequency range of the data signal. On the receive side, after the necessary routine processing of the received signal-noise mixture according to the type of channel used, the signal-noise mixture is divided, in the frequency range of the data signal, into segments having a duration equal to the duration of the symbols and an interval divisibly-equal to the sampling period of the signal-noise mixture. The signal-noise segments are then subjected to an evaluation of their pseudospectrum using the MUSIC method, which consists in analyzing the eigenvalues and eigenvectors of a correlation (covariance) matrix constructed from samples of the signal-noise mixture, and when a pseudospectral peak is detected on a spectral segment corresponding to a given data signal, the transmitted data signal is declared to be present in said segment.