Volterra kernels of bilinear systems have tensor train structure

Goulart, José Henrique de Morais; Burt, P.M.S.

doi:10.23919/eusipco54536.2021.9616311

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2022

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On the Realization of Impulse Invariant Low-Rank Volterra Kernels

Burt

Goulart

2022

IEEE Signal Process. Lett.

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Volterra models can accurately model numerous nonlinear systems of practical interest, but often at an unacceptable computational cost. If the Volterra kernels of a system have low-rank structure (like, e.g., kernels of bilinear systems), this major drawback can in principle be mitigated. Yet, when one seeks an exact discrete-time model of a mixed-signal chain involving that system, the existing formula that generalizes the impulse invariance principle to Volterra kernels yields discretetime kernels that do not share the same low rank. At first sight this would seem to seriously complicate the otherwise simple discrete-time realization of low-rank kernels. We show here that this not the case. By defining a cascade operator, the structure of generalized impulse invariance can be unveiled, leading to a realization without an inordinate increase in computational complexity. Finally, we give a numerical example involving a physical system that shows the relevance of our proposal.

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