Abstract
Consider a time series of signal measurements, x(t), where x has two or more components. This paper shows how to perform nonlinear blind source separation; i.e., how to determine if these signals are equal to linear or nonlinear mixtures of the state variables of two or more statistically independent subsystems. First, the local distributions of measurement velocities are processed in order to derive vectors at each point in x-space. If the data are separable, each of these vectors must be directed along a subspace of \(x \text{-space }\) that is traversed by varying the state variable of one subsystem, while all other subsystems are kept constant. Because of this property, these vectors can be used to construct a small set of mappings, which must contain the “unmixing” function, if it exists. Therefore, nonlinear blind source separation can be performed by examining the separability of the data after they have been transformed by each of these mappings. The method is analytic, constructive, and model-independent. It is illustrated by blindly recovering the separate utterances of two speakers from nonlinear combinations of their audio waveforms.
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Levin, D.N. (2017). Model-Independent Analytic Nonlinear Blind Source Separation. In: Rojas, I., Pomares, H., Valenzuela, O. (eds) Advances in Time Series Analysis and Forecasting. ITISE 2016. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-55789-2_21
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DOI: https://doi.org/10.1007/978-3-319-55789-2_21
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