Abstract: A mud pulse telemetry adaptive noise canceler (ANC) employs a primary transducer and a reference transducer downstream from a position of the primary transducer. The primary transducer receives a primary signal based on a combination of a transmitted pulse and a reflected pulse, and the reference transducer receives a reference signal based on the transmitted pulse. The ANC linearly relates the secondary signal to the primary signal by means of a fast recursive least squares algorithm and calculates a set of weighting coefficients. The finite impulse response (FIR) filter of the ANC uses the set of weighting coefficients to adaptively noise cancel correlated portions between the primary signal and the secondary signal to produce an ANC output signal based on uncorrelated portions between the primary signal and the secondary signal.