Fourier nonlinear filters

Carini, Alberto; Sicuranza, Giovanni L.

doi:10.1016/j.sigpro.2013.06.018

Cited by 83 publications

(60 citation statements)

References 26 publications

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“…Similarly, "CTW" represents the context tree weighting algorithm of [4], "OBR" represents the optimal batch regressor, "VF" represents the truncated Volterra filter [5], "LF" represents the simple linear filter, "B-SAF" and "CR-SAF" represent the Beizer and the Catmul-Rom spline adaptive filter of [6], respectively, "FNF" and "EMFNF" represent the Fourier and even mirror Fourier nonlinear filter of [7], respectively. Finally, "GKR" represents the Gaussian-Kernel regressor and it is constructed using p node regressors, sayd t,1 , .…”

Section: Simulationsmentioning

confidence: 99%

“…. , p. For a fair performance comparison, in the corresponding experiments in Subsections V-E and V-F, the desired data and the regressor vectors are normalized between [−1, 1] since the satisfactory performance of the several algorithms require the Considering the illustrated examples in the respective papers [4], [6], [7], the orders of the FNF and the EMFNF are set to 3 for the experiments in Subsections V-B, V-C, and V-D, 2 for the experiments in Subsection V-E, and 1 for the experiments in Subsection V-F. The order of the VF is set to 2 for all experiments, except for the California housing experiment, in which it is set to 3.…”

Section: Simulationsmentioning

confidence: 99%

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A Comprehensive Approach to Universal Piecewise Nonlinear Regression Based on Trees

Vanli

Kozat

2014

IEEE Trans. Signal Process.

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Abstract-In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an individual sequence manner. We use a tree notion in order to partition the space of regressors in a nested structure. The introduced algorithms adapt not only their regression functions but also the complete tree structure while achieving the performance of the "best" linear mixture of a doubly exponential number of partitions, with a computational complexity only polynomial in the number of nodes of the tree. While constructing these algorithms, we also avoid using any artificial "weighting" of models (with highly data dependent parameters) and, instead, directly minimize the final regression error, which is the ultimate performance goal. The introduced methods are generic such that they can readily incorporate different tree construction methods such as random trees in their framework and can use different regressor or partitioning functions as demonstrated in the paper.Index Terms-Nonlinear regression, nonlinear adaptive filtering, binary tree, universal, adaptive.

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Section: Simulationsmentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

A Comprehensive Approach to Universal Piecewise Nonlinear Regression Based on Trees

Vanli

Kozat

2014

IEEE Trans. Signal Process.

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“…To meet this challenge, one important filter characteristic that needs to be considered is the trade-off between implementation complexity and approximation capability. The well-known Volterra filter [1] represents one extreme of this trade-off, since its universal approximation capability [2][3][4] comes at the cost of a high computational complexity (which is due to the large number of coefficients required for the implementation) [1,[5][6][7][8][9]. In this context, one topic that has drawn attention from researchers in the last decades is the development of Volterra implementations having an enhanced tradeoff between computational complexity and approximation capability.…”

Section: Introductionmentioning

confidence: 99%

A reduced-rank approach for implementing higher-order Volterra filters

Batista

Seara

2016

EURASIP J. Adv. Signal Process.

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The use of Volterra filters in practical applications is often limited by their high computational burden. To cope with this problem, many strategies for implementing Volterra filters with reduced complexity have been proposed in the open literature. Some of these strategies are based on reduced-rank approaches obtained by defining a matrix of filter coefficients and applying the singular value decomposition to such a matrix. Then, discarding the smaller singular values, effective reduced-complexity Volterra implementations can be obtained. The application of this type of approach to higher-order Volterra filters (considering orders greater than 2) is however not straightforward, which is especially due to some difficulties encountered in the definition of higher-order coefficient matrices. In this context, the present paper is devoted to the development of a novel reduced-rank approach for implementing higher-order Volterra filters. Such an approach is based on a new form of Volterra kernel implementation that allows decomposing higher-order kernels into structures composed only of second-order kernels. Then, applying the singular value decomposition to the coefficient matrices of these second-order kernels, effective implementations for higher-order Volterra filters can be obtained. Simulation results are presented aiming to assess the effectiveness of the proposed approach.

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“…Recently, the finite-memory LIP class has been enriched with novel sub-classes of nonlinear filters that guarantee the orthogonality of the basis functions for white uniform input signals in the range ½À1; þ1: the Fourier nonlinear (FN) filters [28,29], the even mirror Fourier nonlinear (EMFN) filters [29,30], and the Legendre nonlinear (LN) filters [31,32]. FN and EMFN filters are based on trigonometric function expansions of the input signal samples, and do not include a linear term among the basis functions.…”

Section: Introductionmentioning

confidence: 99%