A Statistical Test for Impropriety of Complex Random Signals
P.J. Schreier, L.L. Scharf, A. Hanssen, in: Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 2006, pp. 796–799.
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Conference Paper
Author
Schreier, Peter J.;
Scharf, Louis L.;
Hanssen, Alfred
Department
Abstract
A complex random vector is called improper if it is correlated with its complex conjugate. In this paper, we present a generalized likelihood ratio test (GLRT) for impropriety. This test is compelling because it displays the right invariances: The proposed GLR is invariant to linear transformations on the data, including rotation and scaling, just as propriety is preserved by linear transformations. Because canonical correlations make up a complete, or maximal, set of invariants for the Hermitian and complementary covariance matrices under linear transformations, the GLR can be shown to be a function of the squared canonical correlations between the data and its complex conjugate. This validates our intuition that the internal coordinate system should not matter for this hypothesis test
Publishing Year
Proceedings Title
Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process.
Volume
3
Page
796–799
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Cite this
Schreier PJ, Scharf LL, Hanssen A. A Statistical Test for Impropriety of Complex Random Signals. In: Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process. Vol 3. ; 2006:796–799. doi:10.1109/ICASSP.2006.1660774
Schreier, P. J., Scharf, L. L., & Hanssen, A. (2006). A Statistical Test for Impropriety of Complex Random Signals. Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 3, 796–799. https://doi.org/10.1109/ICASSP.2006.1660774
@inproceedings{Schreier_Scharf_Hanssen_2006, title={A Statistical Test for Impropriety of Complex Random Signals}, volume={3}, DOI={10.1109/ICASSP.2006.1660774}, booktitle={Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process.}, author={Schreier, Peter J. and Scharf, Louis L. and Hanssen, Alfred}, year={2006}, pages={796–799} }
Schreier, Peter J., Louis L. Scharf, and Alfred Hanssen. “A Statistical Test for Impropriety of Complex Random Signals.” In Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 3:796–799, 2006. https://doi.org/10.1109/ICASSP.2006.1660774.
P. J. Schreier, L. L. Scharf, and A. Hanssen, “A Statistical Test for Impropriety of Complex Random Signals,” in Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., 2006, vol. 3, pp. 796–799, doi: 10.1109/ICASSP.2006.1660774.
Schreier, Peter J., et al. “A Statistical Test for Impropriety of Complex Random Signals.” Proc.\ IEEE Int.\ Conf.\ Acoustics, Speech and Signal Process., vol. 3, 2006, pp. 796–799, doi:10.1109/ICASSP.2006.1660774.
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