In low-latency applications for 5G and beyond, precise synchronization becomes more challenging. In this correspondence, we generalized the analytical tool to design combined window-filter waveform, which can tolerate imperfect synchronization scenarios. Compared to the previous work focusing on an ideal channel, the generalized tool considers the effect of multipath fading with instantaneous or statistical channel state information at the transmitter (CSIT). The waveform designed by the proposed tool yields lower bit error rates compared to the design with no CSIT and other waveform candidates.