Blind separation of noisy harmonic signals using only second order statistics

We present a robust-to-noise technique for the blind source separation of harmonic signals, using only second order statistics. The mixtures are convolutive and noisy. The noises may be spatially and temporally correlated. Their distributions and correlation functions are unknown. The operations are processed at each frequency bin. Assuming that the correlation and cross-correlation lengths of the noises are finite, we compute non-hermitian interspectral matrices using delayed observations. We show that two of these interspectral matrices are enough to recover the decorrelation matrix. The filtered delayed observations are used again to determine the Givens plane rotations that complete the separation process. The use of higher order statistics is avoided. Wiener filtering is then applied for denoising the outputs. The proposed method is efficient for low Signal to Noise Ratio (SNR), as we show in simulation results