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Communication Dans Un Congrès Année : 2011

Fast Orthogonal Decomposition of Volterra Cubic Kernels using Oblique Unfolding

Résumé

Discrete-time Volterra modeling is a central topic in many application areas and a large class of nonlinear systems can be modeled using high-order Volterra series. The problem with Volterra series is that the number of parameters grows very rapidly with the order of the nonlinearity and the memory in the system. In order to efficiently implement this model, kernel eigen-decomposition can be used in the context of a Parallel-Cascade realization of a Volterra kernel. So, using the multilinear SVD (HOSVD) for decomposing high-order Volterra kernels seems natural. In this paper, we propose to drastically reduce the computational cost of the HOSVD by (1) considering the symmetrized Volterra kernel and (2) exploiting the column-redundancy of the associated mode by using an oblique unfolding of the Volterra kernel. Keeping in mind that the complexity of the full HOSVD for a cubic (I×I×I) unstructured Volterra kernel needs 12I4 flops, our solution allows reducing the complexity to 2I4 flops, which leads to a gain equal to six for a sufficiently large size I.

Dates et versions

hal-00576019 , version 1 (11-03-2011)

Identifiants

Citer

Remy Boyer, Roland Badeau, Gérard Favier. Fast Orthogonal Decomposition of Volterra Cubic Kernels using Oblique Unfolding. ICASSP 2011 - 36th IEEE International Conference on Acoustics, Speech and Signal Processing, 2011, Prague, Czech Republic. ⟨10.1109/icassp.2011.5947249⟩. ⟨hal-00576019⟩
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