Pulse shape design in OFDM serves two (or more) purposes: one is to reduce interchannel intereference caused by Doppler spread due to mobile transmitter/receiver. The other is to reduce out-of-band leakage. In both cases it is important to construct pulse-shapes that satisfy the following properties:

- the pulses are well-localized in time and frequency.
- the pulses are mutually orthonormal (this is not really necessary, if done correctly, but minimizes amplification of AWGN)
- spectral efficiency is as large as possible

I have developed a computationally efficient method for OFDM pulse shape
design that produces mutually orthogonal transmission pulses which
have a prescribed number of taps and show fast spectral decay.
This algorithm has been used successfully in modems for short-radio-wave
communications by * Special Communication Systems *.

An example of the MATLAB pulse shape software is illustrated below: