Name
Abstract | ||
|---|---|---|
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 system. So, using the multilinear SVD (HOSVD) for de composing high-order Volterra kernels seems natural. In this pa per, 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 x I x I) un structured 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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/ICASSP.2011.5947249 | Acoustics, Speech and Signal Processing |
Keywords | Field | DocType |
Volterra series,discrete time systems,eigenvalues and eigenfunctions,nonlinear systems,singular value decomposition,discrete-time Volterra modeling,fast orthogonal decomposition,high-order Volterra series,kernel eigen-decomposition,multilinear SVD,nonlinear systems,oblique unfolding,parallel-cascade realization,unstructured Volterra cubic kernel,Volterra kernel,fast HOSVD,oblique unfolding | Kernel (linear algebra),Singular value decomposition,Mathematical optimization,Nonlinear system,FLOPS,Matrix decomposition,Symmetric matrix,Volterra series,Multilinear map,Mathematics | Conference |
ISSN | ISBN | Citations |
1520-6149 E-ISBN : 978-1-4577-0537-3 | 978-1-4577-0537-3 | 6 |
PageRank | References | Authors |
0.47 | 7 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rémy Boyer | 1 | 301 | 38.10 |
| R. Badeau | 2 | 892 | 63.98 |
| GéRard Favier | 3 | 514 | 46.41 |