Measurements made with at least two sensors (flow rate or pressure) during generation of a message concurrently with operation of a noise source are used to estimate a channel transfer function. The estimated transfer function is then used to attenuate pump noise in a mud pulse telemetry system. It is emphasized that this abstract is provided to comply with the rules requiring an abstract which will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.