Fractional Delay in the Frequency Domain for Beamforming Applications

Various methods for fractional delay in the frequency domain are proposed and discussed as special cases of interpolation applied to audio signal beamforming applications. The techniques for time shifting in the frequency domain are well known, particularly with the discrete Fourier transform. However, the application details for windowed signals, especially for the purpose of time compensation in beamforming applications, have seldom been studied and discussed in the literature. Nowadays, with the growing interest in array processing, fractional delay may be widely applied. The methods discussed are especially suited for frequency processing procedures that consist of windowing + transform with the usual frequency transforms-the discrete Fourier transform (DFT) and the discrete cosine transform (DCT). In parallel, the effects on beamforming precision caused by time-compensation errors when fractional delay is not applied are analyzed for the case of uniform linear microphone arrays.