Balanced parameterization of multichannel blind deconvolutive systems: A continuous time realization

A key problem in multichannel blind deconvolution (MDB) is how to properly model the mixer so that the demixer can be properly modelled correspondingly. This problem naturally triggers one question, viz. how to determine some key model orders, e.g. the number of states, if the problem is analyzed using a state space model. In this paper, to answer this question, we will apply a balanced parameterization approach to a MBD problem with the mixer being modelled as a continuous time linear time invariant (LTI) system. Besides allowing the determination of the number of states required in the demixer, compared with the controller canonical form representation or the observer canonical form representation of the LTI continuous time system, our approach has also the advantages of numerical robustness. The proposed method is validated through practical examples using speech signals and electroencephalographic (EEG) data.