Convolutive blind signal separation via polynomial matrix generalised eigenvalue decomposition

• Published in: Electronics letters Vol. 53; no. 2; pp. 87 - 89
• Main Author: Redif, S
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 19.01.2017
• Subjects: blind source separation; Computer simulation; computer simulations; convolution; convolutive blind signal separation; Decomposition; Eigenvalues; eigenvalues and eigenfunctions; Electronics; Hermitian matrices; Information and communications; Intervals; matrix decomposition; paraHermitian matrices; polynomial GEVD; Polynomial matrices; polynomial matrix generalised eigenvalue decomposition; Polynomials; Signal processing; source nonstationarity; source signals; paraHermitian matrices; matrix decomposition; polynomial matrix generalised eigenvalue decomposition; source nonstationarity; computer simulations; Hermitian matrices; eigenvalues and eigenfunctions; polynomial matrices; polynomial GEVD; source signals; convolution; convolutive blind signal separation; blind source separation
• ISSN: 0013-5194; 1350-911X; 1350-911X
• DOI: 10.1049/el.2016.3200

An extension of the generalised eigenvalue decomposition (GEVD) to polynomial matrices, that is, a polynomial GEVD is proposed. A method for its application to convolutive blind signal separation is then introduced. The author shows that the source signals can be estimated using two related, but different, ‘target’ polynomial matrices. These polynomial matrices are parahermitian matrices, corresponding to two different signal time intervals, which capture the non-stationarity of the sources. The validity of our method in separating the sources from their convolutive mixtures is demonstrated with computer simulations.