Proof of Wiener-like linear regression of isotropic complex symmetric alpha-stable random variables

Roland Badeau (1, 2) , Antoine Liutkus (3)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 TSI - Département Traitement du Signal et des Images
3 PAROLE - Analysis, perception and recognition of speech

This document features supplementary materials to the reference paper [1]. It provides the proof of equation (8) in [1]. This proof concerns a particular regression property of complex isotropic symmetric alpha-stable random variables (see [2]). In [1], this property is shown paramount in building efficient filters for separating symmetric alpha-stable processes. Such processes exhibit very large dynamic ranges while being locally stationary, and have been shown appropriate for audio modeling.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Roland Badeau, Antoine Liutkus. Proof of Wiener-like linear regression of isotropic complex symmetric alpha-stable random variables. 2014. ⟨hal-01069612⟩