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Mud pulse telemetry is a method used for measurement-while-drilling (MWD) in the oil industry. Information (tool-face orientation, temperature, pressure etc.) is sent from the bottom of the well to the surface by means of pressure waves in the drilling fluid (the drilling mud). It is shown that adaptive equalization of the received MSK pressure waveform is possible using methods commonly used in telephone modems, cellular telephones and acoustic telemetry systems. A passband complex fractionally-spaced decision-feedback equalizer, using a weighted LS algorithm for updating the coefficients, is shown to give good results in reducing signal distortion.