A zero-cumulant random variable and its applications

Abstract : High Order Statistics (HOS) are widely used in many algorithms ranging from blind identification to signal separation. A well-known identifiability result is that at most one Gaussian source should be present in static mixtures [J. Eriksson, V. Koivunen, Identifiability, separability and uniqueness of linear ICA models, IEEE Signal Process. Lett. (2004) 601-604]. The reason for this is that these algorithms utilize cumulants of order higher than two, and that they are all null for circular Gaussian random variables [M. Kendall, A. Stuart, The Advanced Theory of Statistics, Distribution Theory, vol. 1, C. Griffin, 1977]. Simple examples of non-Gaussian complex random variables having zero cumulants of order three to seven are given, which can be encountered in the real world.
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Nicolas Petrochilos, Pierre Comon. A zero-cumulant random variable and its applications. Signal Processing, Elsevier, 2006, 86 (11), pp.3334 - 3338. ⟨10.1016/j.sigpro.2006.02.023⟩. ⟨hal-01693671⟩

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