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Mixed third- and fourth-order cumulants-based algorithm for nonlinear kernels identification in cubic systems

Zidane, M. ; Dinis, R.

Springer Signal, Image and Video Processing Vol. 2021, Nº 9, pp. 1 - 10, September, 2021.

ISSN (print):
ISSN (online): 1863-1703

Scimago Journal Ranking: 0,41 (in 2020)

Digital Object Identifier: 10.1007/s11760-021-02004-2

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Abstract
Ignoring nonlinear effects in many practical situations degrades the performance. This paper considers nonlinear system characterization using higher-order cumulants and polyspectra. A novel method to blindly identify the kernels of cubic systems using mixed third- and fourth-order cumulants is developed. We study the link between the Fourier transform of third-order and fourth-order cumulants in nonlinear cubic systems. Then, we use the inverse Fourier transform to build a new formula which combines third- and fourth-order cumulants. Then, we generalize it to the nth-order cumulants and the kernels of nonlinear cubic systems driven by a non-Gaussian random signal, independent, identically distributed (i.i.d.) in Gaussian noise environment. Our performances results indicate that the proposed approach is able to identify blindly the kernels in cubic systems.