Effecting frequency shifts with a DFT filterbank

It is often required to apply a shift in frequency to the channelised data within a DFT filterbank. An example application is the frequency domain implementation of the cyclic Wiener filter. A common approach is to rotate the transform through an appropriate number of bins, but this is only accurate if the frequency shift is a multiple of the bin width. A better approach is to combine the bin rotation with an approximate fine shift. The exact solution is found for an arbitrary DFT filterbank and novel, computationally efficient approximations to this are derived and compared.