## Abstract

In this paper we consider blind source separation (BSS) problem of signals with are spatially uncorrelated of order four, but temporally correlated of order four (for instance speech or biomedical signals). For such type of signals we propose a new sufficient condition for separation using fourth order statistics, stating that the separation is possible, if the source signals have distinct normalized cumulant functions (depending on time delay). Using this condition we show that the BSS problem can be converted to a symmetric eigenvalue problem of a generalized cumulant matrix Z^{(4)} (b) depending on L-dimensional parameter b, if this matrix has distinct eigenvalues. We prove that the set of parameters b which produce Z^{(4)} (b) with distinct eigenvalues form an open subset of R^{L}, whose complement has a measure zero. We propose a new separating algorithm which uses Jacobi's method for joint diagonalization of cumulant matrices depending on time delay. We emphasize the following two features of this algorithm: 1) The optimal number of matrices for joint diago- nalization is 100-150 (established experimentally), which for large dimensional problems is much smaller than those of JADE; 2) It works well even if the signals from the above class are, additionally, white (of order two) with zero kurtosis (as shown by an example).

Original language | English |
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Pages (from-to) | 573-579 |

Number of pages | 7 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E86-A |

Issue number | 3 |

Publication status | Published - Mar 2003 |

Externally published | Yes |

## Keywords

- Blind source separation
- Cumulant functions
- Eigenvalue decomposition
- Independent component analysis
- Join diagonalization