Abstract: In a multiple response digital data transmission system the signal processing, which results in the generation of a plurality of time spaced pulses from each signal element and the superimposition of those pulses which occur simultaneously, is carried out in the receiver, possibly after demodulation. The signal processing may be performed by a transversal filter having circuits connected to tappings of a delay line, which circuits have gains chosen in accordance with the desired multiple response characteristics. The transversal filter may include additional circuits which are adaptive and controlled in response to the departure of the levels of the superimposed pulses from reference levels to correct for signal distortions arising during transmission. The transmitted data may be precoded in dependence upon the multiple response characteristics used so that relatively little processing is required after transmission through the system to restore the data to its original form.