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On the realization of impulse invariant low-rank Volterra kernels

Phillip Mark Seymour Burt José Henrique de M Goulart 1 
1 IRIT-SC - Signal et Communications
IRIT - Institut de recherche en informatique de Toulouse
Abstract : 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 discrete-time 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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Submitted on : Tuesday, June 21, 2022 - 6:34:17 PM
Last modification on : Monday, July 4, 2022 - 9:10:31 AM
Long-term archiving on: : Thursday, September 22, 2022 - 8:04:42 PM


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Phillip Mark Seymour Burt, José Henrique de M Goulart. On the realization of impulse invariant low-rank Volterra kernels. IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, In press, ⟨10.48550/arXiv.2107.06144⟩. ⟨hal-03701232⟩



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