Reconstruction of discrete-time signals from a subset of weighted DFT outputs

An algorithm is presented for combining the output of DFT bins to produce a single discrete-time signal, where , the DFT size. The technique described compensates for the effect of any weighting function used in the original DFT, as well as any DFT overlap fraction. The output sampling rate can be selected appropriate to the bandwidth of the resulting signal. The procedure reconstructs the minimum-energy signal which would produce the observed DFT outputs, knowing the weighting function and overlap fraction. Implementation of the algorithm requires multiplication of a complex -vector (the bin outputs) by an rxr complex matrix, to produce discrete-time samples for a single input DFT. This multiplication is performed on successive DFT\´s to produce the output sequence, with sampling rate times that of each DFT bin.