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This paper describes a method of transmitter waveform generation which leads to an optimally "narrow" pulse at the receiver of a given linear time invariant digital communications channel. The resulting transmitter waveform is realizable in that it must be identically zero before . The instant at which the received pulse must have its peak may be specified. Two examples are given: the first is a purely analytic application to a first-order low-pass filter channel; the second demonstrates that the optimum transmitter waveform can be produced experimentally even when the phase characteristics of the channel are unknown and the channel amplitude response is known only empirically. It is seen that the transmitter waveform has the effect of equalizing both the channel amplitude response and the channel phase response. The basic method for phase equalization is recognized as time reversal, a presently practised method. Comparable theoretical works from the literature are discussed.