Abstract: An apparatus and method for restoring digital pulses within a data transmission system which have degraded due to the attenuation and distortion inherent in a data transmission medium. The apparatus comprises an adaptive equalizer which receives signals from the data transmission medium, while the method by which the digital pulses are restored comprises: storing plural equalizer transfer function control values in a memory, passing the signal through an equalizer having a controllable transfer function, comparing a characteristic of the output signal of the equalizer with a reference signal and producing a difference signal, using the difference signal to select a set of stored transfer function control values from the memory, controlling the equalizer from the selected transfer function control values so as to minimize their difference from the reference signal. This apparatus and method are suitable for high-speed applications such as T1 and E1, requiring minimal configuration by the user.