A system for eliminating the tool mode signal from a received combined signal comprising both tool mode and formation mode components, comprising: a formation receiver for receiving said combined signal, a reference receiver for receiving a tool mode reference signal, a filter for processing said tool mode reference signal and generating a predicted tool mode component of the combined signal, and a summation element for subtracting said predicted tool mode component from said combined signal and generating a predicted formation mode component. The filter preferably incorporates a portion of the output of the summation element as an error signal, enabling the filter to adapt to changing conditions and update the algorithm on which it makes its predictions. According to an alternative system, an average value for the tool mode signal is updated according to a moving average to which new data points are added as they become available. Tool mode signals are distinguishable from signals having both components because they have lower energies. When a signal is received having the lower energy that is indicative of the absence of a formation mode signal, the data point is treated as a purely tool mode signal and is added to the moving average.