1. An apparatus for converting L binary digital incoming channels, wherein the frequency spectra occupied by each channel includes multiple first and second side bands, to an L channel frequency division multiplexed (FDM) signal, said apparatus being of the type wherein a different first side band from each binary digital channel is selected by filtering, and the filtered signals are combined to form an FDM signal, comprising: first positioning means for shifting the frequency spectra of adjacent channels relative to one another until the first side bands in adjacent channels are non-overlapping; first digital filtering means for removing the second side bands from the frequency spectrum of each digital channel; first Fast Fourier Transform (FET) process means for receiving the output of said first digital filtering means and passing only a single different one of the remaining first side bands in each channel, said first FFT processing means storing the information from said L filtered channels as an array of samples in an FFT output memory; and first weighting means for receiving said samples from said FFT memory, multiplying each of said samples by an appropriate value and combining said multiplied samples in order to form a digital FDM signal.