Pulse shaping, as it is done today, is an effort to fix fidelity issues caused by the transmitting amplifier since high power amplifiers do a poor job duplicating the input signal without distortions.  More specifically, due to the transient response of the amplifier, the output will over shoot, ring and droop, introducing undesired low and high frequency components into other parts of the spectrum. One such example is using a pseudo random Gaussian shape for the RF input signal thus slowing the rise and fall time of the RF input pulse. The trade off with Gaussian shaping is it limits duty cycles. Other methods approach the problem in a calibration-like process, specific to the amplifier, where the error between the RF input and amplifier output is digitized and the inverse error function is post processed and applied to the original, and ported to an arbitrary waveform generator. This solution is not real time, is laborious, and is specific to one amplifier and one input RF pulse shape.