Inversion of the sliding Fourier transform using only two frequency bins and its application to source separation

In this paper we show that the Fourier transform can be inverted using only two frequency bins when it is computed over sliding windows with one-point delay and the window length is less than the number of frequencies. This two conditions allow to recover the time-domain signal by multiplying the frequency-domain signal times a 2 × 2 invertible matrix. We also show how this result can be used to separate convolutive mixtures of signals with a reduced computational cost.

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