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

Authors:
A. Dapena;C. Servière;L. Castedo
Affiliations:
Departamento de Electrónica y Sistemas, Universidad de La Coruña, Campus de Elviña s/n, 15.071 La Coruña, Spain;LIS-ENSIEG, BP 46, 38402 Saint Martin d'Heres Cedex, France;Departamento de Electrónica y Sistemas, Universidad de La Coruña, Campus de Elviña s/n, 15.071 La Coruña, Spain
Venue:
Signal Processing
Year:
2003

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Abstract

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.