# Cross-term elimination in parallel wiener systems using a linear input transformation

M. Schoukens, Y. Rolain

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)

## Abstract

Multivariate polynomials are often used to model nonlinear behavior, e.g., in parallel Wiener models. These multivariate polynomials are mostly hard to interpret due to the presence of cross terms. These polynomials also have a high amount of coefficients, and the calculation of an inverse of a multivariate polynomial with cross terms is cumbersome. This paper proposes a method to eliminate the cross terms of a multivariate polynomial using a linear input transformation. It is shown how every homogeneous polynomial described using tensors can be transformed to a canonical form using multilinear algebraic decomposition methods. Such tensor decomposition methods have already been used in nonlinear system modeling to reduce the complexity of Volterra models. Since every polynomial can be written as a sum of homogeneous polynomials, this method results in a decoupled description of any multivariate polynomial, allowing a model description that is easier to interpret, easier to use in a design, and easier to invert. This paper first describes a method to represent and decouple multivariate polynomials using tensor representation and tensor decomposition techniques. This method is applied to a parallel Wiener model structure, where a multiple-input-single-output polynomial is used to describe the static nonlinearity of the system. A numerical example shows the performance of the proposed method.

Original language English 6126025 845-847 3 IEEE Transactions on Instrumentation and Measurement 61 3 https://doi.org/10.1109/TIM.2011.2174851 Published - 1 Mar 2012 Yes

## Keywords

• Decoupling
• Input transformation
• Multivariate
• Parallel Wiener
• Polynomial
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