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arXiv · 1703.06417

Spectral analysis of stationary random bivariate signals

Julien Flamant·Nicolas Le Bihan·Pierre Chainais
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Abstract

A novel approach towards the spectral analysis of stationary random bivariate signals is proposed. Using the Quaternion Fourier Transform, we introduce a quaternion-valued spectral representation of random bivariate signals seen as complex-valued sequences. This makes possible the definition of a scalar quaternion-valued spectral density for bivariate signals. This spectral density can be meaningfully interpreted in terms of frequency-dependent polarization attributes. A natural decomposition of any random bivariate signal in terms of unpolarized and polarized components is introduced. Nonparametric spectral density estimation is investigated, and we introduce the polarization periodogram of a random bivariate signal. Numerical experiments support our theoretical analysis, illustrating the relevance of the approach on synthetic data.

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Julien Flamant, Nicolas Le Bihan, Pierre Chainais. 2017-03-19. Spectral analysis of stationary random bivariate signals. https://doi.org/10.1109/tsp.2017.2736494

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