Measuring a linear approximation to weakly nonlinear MIMO systems

Tadeusz Dobrowiecki, Joannes Schoukens

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


The paper addresses the problem of preserving the same LTI approximation of a nonlinear MIMO (multiple-input multiple-output) system. It is shown that when a nonlinear MIMO system is modeled by a multidimensional Volterra series, periodic noise and random multisines are equivalent excitations to the classical Gaussian noise, in a sense that they yield in the limit, as the number of the harmonics M -> infinity, the same linear approximation to the nonlinear MIMO system. This result extends previous results derived for nonlinear SISO (single-input single-output) systems. Based upon the analysis of the variability of the measured FRF (frequency response function) due to the presence of the nonlinearities and the randomness of the excitations, a new class of equivalent input signals is proposed, allowing for a lower variance of the nonlinear FRF measurements, while the same linear approximation is retrieved.
Original languageEnglish
Pages (from-to)1737-1751
Number of pages15
Publication statusPublished - 1 Oct 2007


  • Volterra MIMO systems
  • Nonparametric frequency response
  • random multisines
  • Orthgogonal multisines


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