What technique minimizes the bandwidth of a PSK31 signal?

PSK31 is designed to be an incredibly narrow digital mode, occupying only about 31 Hz of bandwidth. To achieve this, the transitions between phase states must be as smooth as possible, because abrupt, square transitions would create high-frequency harmonics that widen the signal. By using sinusoidal data pulses, the equipment smoothly ramps the signal's amplitude down to zero, shifts the phase, and then smoothly ramps it back up. This sinusoidal shaping virtually eliminates the broad harmonics that would otherwise be caused by sharp keying, thus minimizing the overall bandwidth.