Frequency domain quaternion adaptive filters: Algorithms and convergence performance

Recently, adaptive filtering was extended to quaternion-valued systems. Quaternion-valued algorithms exhibit improved geometrical properties compared with real- and complex-valued algorithms. Moreover, working in the frequency domain allows a fast execution along with a good convergence performance....

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Bibliographic Details
Published in:Signal processing Vol. 136; pp. 69 - 80
Main Authors: Ortolani, Francesca, Comminiello, Danilo, Scarpiniti, Michele, Uncini, Aurelio
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2017
Subjects:
Adaptive Filters
Frequency Domain
Hypercomplex
Quaternion-Valued Adaptive Filtering
Quaternions
Adaptive Filters
Hypercomplex
Quaternions
Frequency Domain
Quaternion-Valued Adaptive Filtering
ISSN:0165-1684, 1872-7557
Online Access:Get full text
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Summary:Recently, adaptive filtering was extended to quaternion-valued systems. Quaternion-valued algorithms exhibit improved geometrical properties compared with real- and complex-valued algorithms. Moreover, working in the frequency domain allows a fast execution along with a good convergence performance. In this work, we propose three different quaternion-valued adaptive algorithms operating in the frequency domain. Convergence properties are also analyzed: in particular, the step size stability range is obtained in relation to the eigenvalues of the input autocorrelation matrix and the Excess Mean Square Error (EMSE) is expressed in relation to the algorithm parameters. Finally, simulations support the proposal.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2016.11.002