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• W2558768576 abstract "The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued signal into its quadrature component. In this paper, we define a probabilistic generalization of this approach. We model the observable real-valued signal as the real part of a latent complex-valued Gaussian process. In order to obtain the appropriate statistical relationship between its real and imaginary parts, we define two new classes of complex-valued covariance functions. Through an analysis of simulated chirplets and stochastic oscillations, we show that the resulting Gaussian process complex-valued signal provides a better estimate of the instantaneous amplitude and frequency than the established approaches. Furthermore, the complex-valued Gaussian process regression allows to incorporate prior information about the structure in signal and noise and thereby to tailor the analysis to the features of the signal. As a example, we analyze the non-stationary dynamics of brain oscillations in the alpha band, as measured using magneto-encephalography." @default.
• W2558768576 created "2016-12-08" @default.
• W2558768576 creator A5039391126 @default.
• W2558768576 creator A5091232686 @default.
• W2558768576 date "2016-11-30" @default.
• W2558768576 modified "2023-09-27" @default.
• W2558768576 title "Complex-valued Gaussian Process Regression for Time Series Analysis" @default.
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• W2558768576 hasPublicationYear "2016" @default.
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