The discrete Fourier transform (DFT) can be used as a precoding technique in a filter bank system to partially recover complex orthogonality. In this work, a proposal is made to make the waveform design more flexible through the introduction of a parameter called rate factor. With this parameter, we generalize the DFT precoded filter bank system and modify the data transmission format when compared to the conventional system. Such modification allows for better resource allocation and lower PAPR. Furthermore, theoretical and simulation results show better error performance in high mobility scenarios.