Testing for nonlinearity in time series: the method of surrogate data
Conference proceedings on Interpretation of time series from nonlinear mechanical systems
Physica D
An Analysis of the Fundamental Structure of Complex-Valued Neurons
Neural Processing Letters
Sequential Data Fusion via Vector Spaces: Fusion of Heterogeneous Data in the Complex Domain
Journal of VLSI Signal Processing Systems
An adaptive approach for the identification of improper complex signals
Signal Processing
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Although the emergence of multivariate signals in natural sciences and engineering has emphasised the problem of signal representation, that is, whether signals are by their nature a set of independent observations or multidimensional vectorial quantities, little research has been conducted on detecting the true nature of such signals. It remains unclear, therefore, when the complex-valued approach is to be preferred over the bivariate one, thus, clearly indicating the need for a criterion that addresses this issue. To this cause, we propose a nonparametric statistical test, based on the local predictability in the complex-valued phase space, which discriminates between the bivariate and complex-valued nature of time series. This is achieved in the well-established surrogate data framework. Results on both benchmark and real-world IPIX radar data support the approach.