Abstract: Filters are provided at the outputs of data transmission links to overcome attenuation distortion and phase distortion but such filters tend to increase the noise content of received signals. In the present invention a filter coupled to a linear baseband channel is constrained to be an all pass network, thus avoiding any noise enhancement at its output. The filter is adjusted using a channel estimator and an adjustment system to give the channel plus the filter an impulse-response that rises rapidly to its peak, thus simplifying the detection process needed for a satisfactory tolerance to noise.