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A Complete Framework for Linear Filtering of Bivariate Signals

Abstract : A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms of their eigenproperties enabling compact calculus and physically interpretable filtering relations in the frequency domain. The design of filters exhibiting fundamental properties of polarization optics (birefringence and diattenuation) is straightforward. It yields an efficient spectral synthesis method and new insights on Wiener filtering for bivariate signals with prescribed frequency-dependent polarization properties. This generic framework facilitates original descriptions of bivariate signals in two components with specific geometric or statistical properties. Numerical experiments support our theoretical analysis and illustrate the relevance of the approach on synthetic data.
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Contributor : Nicolas Le Bihan Connect in order to contact the contributor
Submitted on : Wednesday, February 13, 2019 - 1:31:09 PM
Last modification on : Wednesday, November 3, 2021 - 6:41:47 AM

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Julien Flamant, Pierre Chainais, Nicolas Le Bihan. A Complete Framework for Linear Filtering of Bivariate Signals. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2018, 66 (17), pp.4541-4552. ⟨10.1109/TSP.2018.2855659⟩. ⟨hal-02017824⟩



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