Blind separation algorithm for speech and noise based on diagonalizing second-order statistics accurately

A blind source separation algorithm by the accurate diagonalization of second-order statistics is presented for the mixed speech-noise signals. The new algorithm uses the autocorrelation covariance matrix and its one-sample delayed counterpart of the two prewhitened noisy data and forms two 2×2 positive definite symmetry matrices pencil. A tangent algorithm for computing the generalized singular value decomposition is then exploited for simultaneously diagonalizing these two matrices accurately, and its theoretic proof is also presented. Compared with JADE algorithm and SOBI algorithm, the new algorithm is of simple computation and more computation precision. And it overcomes the limitations of their both incapable accurate diagonalization for fourth-order cumulant matrices and time-delayed covariance matrices, separately. Under the conditions of white Gaussian and colored noise, computer simulation results show that the performance of the new algorithm separating speech from noisy data is superior to those of JADE algorithm and SOBI algorithm.