A Sparse-Interpolated Scheme for Implementing Adaptive Volterra Filters

Batista, Eduardo Luiz Ortiz; Tobias, Orlando J.; Seara, Rui

doi:10.1109/tsp.2009.2036480

Cited by 46 publications

(33 citation statements)

References 21 publications

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“…The large number of coefficients required to implement Volterra filters can be reduced by exploiting the redundancy of part of the coefficients of the standard nonlinear kernels [1,15]. Such redundancy arises from the fact that coefficients with permutated indices (e.g., h 2(0,1) and h 2(1,0) ) are multiplied by the same cross product of the input signal (e.g., x(n)x(n − 1) in the case of h 2(0,1) and h 2(1,0) ) when the kernel output is evaluated.…”

Section: Redundancy-removed Implementationmentioning

confidence: 99%

“…Such representation of the kernel input-output relationship, known as triangular [1] or even redundancy-removed [15] representation, results in a number of coefficients given by…”

Section: Redundancy-removed Implementationmentioning

confidence: 99%

“…Examples of these implementations are the Volterra delay filter [10], the power filter [11], and general diagonally-pruned implementations [12][13][14]. Other approaches combine interpolation and sparse implementations for the sake of performance [15][16][17]. Frequency-domain approaches also have been used for obtaining effective reduced-complexity Volterra implementations [18,19].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Redundancy-removed Implementationmentioning

confidence: 99%

“…Such representation of the kernel input-output relationship, known as triangular [1] or even redundancy-removed [15] representation, results in a number of coefficients given by…”

Section: Redundancy-removed Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Batista

Seara

2016

EURASIP J. Adv. Signal Process.

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“…The filters find application in speech [1], audio [2,3], telecommunication [4], image processing [1], biological system modeling [5], and many other fields. The LIP class includes truncated Volterra filters [1], still actively studied and used in applications [6][7][8][9][10], but also Wiener nonlinear filters [1], Hammerstein filters [1,[11][12][13][14], memory and generalized memory polynomial filters [15,16], filters based on functional expansions of the input samples, as functional link artificial neural networks (FLANN) [17][18][19][20] and radial basis function networks [21]. A review of finite-memory LIP nonlinear filters can be found in [22].…”

Section: Introductionmentioning

confidence: 99%

A study about Chebyshev nonlinear filters

Carini

Sicuranza

2016

Signal Processing

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“…The class is characterized by the property that the filter output depends linearly on the filter coefficients. Among LIP filters, the most popular are the truncated Volterra filters [1], still actively studied and used in applications [2, 3,4,5,6,7,8,9]. Other elements of the class include particular cases of Volterra filters, as the Hammerstein filters [1, 10,11,12,13], and modified forms of Volterra filters, as memory and generalized memory polynomial filters [14,15].…”

Section: Introductionmentioning

confidence: 99%

Introducing Legendre nonlinear filters

Carini

Cecchi

Gasparini

et al. 2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper introduces a novel sub-class of linear-in-the-parameters nonlinear filters, the Legendre nonlinear filters. Their basis functions are polynomials, specifically, products of Legendre polynomial expansions of the input signal samples. Legendre nonlinear filters share many of the properties of the recently introduced classes of Fourier nonlinear filters and even mirror Fourier nonlinear filters, which are based on trigonometric basis functions. In fact, Legendre nonlinear filters are universal approximators for causal, time invariant, finite-memory, continuous, nonlinear systems and their basis functions are mutually orthogonal for white uniform input signals. In adaptive applications, gradient descent algorithms with fast convergence speed and efficient nonlinear system identification algorithms can be devised. Experimental results, showing the potentialities of Legendre nonlinear filters in comparison with other linear-in-theparameters nonlinear filters, are presented and commented.

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A Sparse-Interpolated Scheme for Implementing Adaptive Volterra Filters

Cited by 46 publications

References 21 publications

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

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

A study about Chebyshev nonlinear filters

Introducing Legendre nonlinear filters

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