A system and method for reducing noise from a signal during drilling of a well. A system for generating mechanical vibrations may generate acoustic signals for communicating information, and may induce pressure signals in a drilling mud communicating information. A noise reduction system may receive both the acoustic and pressure signals and phase shift one set of signals to adjust for a time difference between the two. The system may also sample the signals and may overlay the signals or the sampled signals and cancel the noise from the received signals.