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This paper studies the problem of blind separation of convolutively mixed source signals on the basis of the joint diagonalization (JD) of power spectral density matrices (PSDMs) observed at the output of the separation system. Firstly, a general framework of JD-based blind source separation (BSS) is reviewed and summarized. Special emphasis is put on the separability conditions of sources and mixing system. Secondly, the JD-based BSS is generalized to the separation of convolutive mixtures. The definition of a time and frequency dependent characteristic matrix of sources allows us to state the conditions under which the separation of convolutive mixtures is possible. Lastly, a frequency-domain approach is proposed for convolutive mixture separation. The proposed approach exploits objective functions based on a set of PSDMs. These objective functions are defined in the frequency domain, but are jointly optimized with respect to the time-domain coefficients of the unmixing system. The local permutation ambiguity problems, which are inherent to most frequency-domain approaches, are effectively avoided with the proposed algorithm. Simulation results show that the proposed algorithm is valid for the separation of both simulated and real-word recorded convolutive mixtures.

A new technique for the blind separation of convolutive mixtures is proposed in this paper. Inspired by the works of Amari, Sabala , and Rahbar, we firstly start from the application of Kullback-Leibler divergence in frequency domain, and then we integrate Kullback-Leibler divergence over the whole frequency range of interest to yield a new objective function which turns out to be time-domain variable dependent. In other words, the objective function is derived in frequency domain which can be optimized with respect to time domain variables. The proposed technique has the advantages of frequency domain approaches and is suitable for very long mixing channels, but does not suffer from the local permutation problem as the separation is achieved in time-domain.

This paper studies the problem of blind separation of convolutive mixtures by means of Kullback-Leibler divergence in frequency domain. Unlike exiting approaches, an integrated objective function is defined in frequency-domain with time-domain parameters as the variables. The permutation problem is avoided through the frequency domain integration and time domain optimization. Simulation results show that the algorithm is valid and of high performance for the separation of real world recorded convolutive mixtures.