A transmitter and corresponding method for transmitting an OFDM signal in a communications channel, including a plurality of base-band OFDM modulators, each for modulating a respective data signal onto a plurality of orthogonal sub-carriers and outputting a respective sub-channel OFDM signal; and a fast convolution filter and up-converter for applying fast convolution filtering and digital up-conversion to the sub-channel OFDM signals to output a combined OFDM signal that includes each of the sub-channel OFDM signals, the fast convolution and up-converter filtering each of the sub-channel OFDM signals and frequency shifting all of the sub-channel signals to respective designated frequencies within the combined OFDM signal. A corresponding receiver is also provided.