Apparatus for and a method of digital signal processing utilises a technique known as sub-band decomposition and reconstruction. A plurality of input channels are provided each of which is mixed with a vernier frequency correction. In a multiplexer implementation, an FFT weighted overlap-add demultiplexer (c) is provided for decomposing each input channel into sub-bands. The sub-band outputs are decimated by a factor (d) to the common input sampling rate of a multiplexer, the sub-bands from each channel then being passed into the appropriate ports of an FFT weighted overlap-add multiplexer (f) by means of a switch matrix (e). The multiplexer (f) reconstructs the individual channels, interpolates each channel up to the output sampling rate of the FDT signal, mixes each channel up to its assigned carrier frequency in the FDM and multiplexes the channels. This provides a computationally efficient architecture with the flexibility to accommodate channels of differing bandwidths.