This article addresses identification of nonlinear systems represented by Volterra series. To improve the robustness of some existing methods, we propose a pre-processing stage that separates nonlinear homogeneous order contributions from which Volterra kernels can be identified independently. Unlike existing separation methods that use amplitude relations between test signals, we propose another order separation method based on phase. This method gives access to a new type of complex-valued output signals, which can be used to improve kernel identification. First, the underlying ideas are introduced via the presentation of a theoretical method using complex-valued test signals. Second the proposed order separation method using real-valued signals is described. Third, a new identification process is given, combining existing leastsquares identification method with the previous results. Finally, numerical experiments are used to compare the proposed order separation method with state-of-the art, as well as to evaluate the new Volterra series identification process.

This article addresses the identification of nonlinear systems represented by Volterra series. To improve the robustness of state-of-the-art estimation methods, we introduce the notion of "homophase signals", for which a separation method is given. Those homophase signals are then used to derive a robust identification process. This prior step is similar to nonlinear homogeneous order separation, in which amplitude relations are used to separate the orders of a Volterra series, but offers a better conditioning by using phase deviations rather than amplitudes. First an academic phase-based method using complex-valued test signals is introduced for separating nonlinear orders. Second this notion of phase deviation is extended to real-valued signals, which leads to the design of the proposed homophase signals separation method. Finally, a new identification process is derived using the homophase signals. Simulations are used to highlight the benefits of the proposed identification process in comparison to the standard approach.

This paper introduces a constrained source/filter model for semisupervised speech separation based on non-negative matrix factorization (NMF). The objective is to inform NMF with prior knowledge about speech, providing a physically meaningful speech separation. To do so, a source/filter model (indicated as Instantaneous Mixture Model or IMM) is integrated in the NMF. Furthermore, constraints are added to the IMM-NMF, in order to control the NMF behaviour during separation, and to enforce its physical meaning. In particular, a speech specific constraint-based on the source/filter coherence of speech-and a method for the automatic adaptation of constraints' weights during separation are presented. Also, the proposed source/filter model is semi-supervised: during training, one filter basis is estimated for each phoneme of a speaker; during separation, the estimated filter bases are then used in the constrained source/filter model. An experimental evaluation for speech separation was conducted on the TIMIT speakers database mixed with various environmental background noises from the QUT-NOISE database. This evaluation showed that the use of adaptive constraints increases the performance of the source/filter model for speaker-dependent speech separation, and compares favorably to fully-supervised speech separation.

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