A study about Chebyshev nonlinear filters

Carini, Alberto; Sicuranza, Giovanni L.

doi:10.1016/j.sigpro.2015.11.008

Cited by 37 publications

(13 citation statements)

References 44 publications

(59 reference statements)

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“…Mirror Fourier [31,32], Legendre [33], and Chebyshev [34] nonlinear filters, we show in this paper that WN filters admit perfect periodic sequences (PPSs). The PPSs are periodic sequences that guarantee a perfect orthogonality of the basis functions of a certain nonlinear filter over a period of the sequence.…”

Section: Introductionmentioning

confidence: 76%

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Nonlinear system identification using Wiener basis functions and multiple-variance perfect sequences

et al. 2019

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The paper addresses nonlinear identification using the Wiener series. Differently from the traditional approach, the truncated Wiener series is expressed as a linear combination of basis functions, which are orthogonal for white Gaussian inputs. The coefficients of the basis functions are efficiently estimated with the cross-correlation method, computing the cross-correlation between the basis functions and the system output. Perfect periodic sequences (PPSs), which are periodic sequences guaranteeing the perfect orthogonality of the basis functions over a period, are also developed. The PPSs allow to avoid the estimation problems experienced with the cross-correlation method using stochastic inputs. The Wiener series formulation in terms of basis functions allows also to develop a novel, more efficient, multiple-variance identification method. Multiple-variance methods exploit input signals with multiple variances for estimating the Volterra kernels. They overcome the problem of locality of the solution, i.e., the fact that the identified model well approximates the nonlinear system only for input signal variances close to that used for the identification. Optimal values of the multiple variances are also studied in the paper. Experimental results, involving the identifications of real devices, show that the

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Section: Introductionmentioning

confidence: 76%

“…The approach followed in this paper differs from [32,46,53], where PPSs for even mirror Fourier, Legendre, and Chebyshev filters were obtained.…”

Section: Perfect Periodic Sequencesmentioning

confidence: 99%

Nonlinear system identification using Wiener basis functions and multiple-variance perfect sequences

et al. 2019

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“…Moreover, it is important to highlight that the reduction in the number of coefficients from (8) to (10) obtained by using the redundancy-removed implementation comes without loss of generality (i.e., a given kernel can be equivalently implemented by using either the standard or the redundancy-removed implementation). As in the case of the standard Volterra kernels, the input-output relationship of the redundancy-removed ones can also be represented in vector form.…”

Section: Redundancy-removed Implementationmentioning

confidence: 99%

“…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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“…Perfect periodic sequences (PPSs) [9], [10] have been proposed for linear [11], [12] and nonlinear [8], [13]- [17] system identification as an alternative to stochastic inputs. A PPS ensures that the cross-correlation between any two different basis functions of the system, estimated over a period, is zero.…”

Section: Introductionmentioning

confidence: 99%

Multivariance nonlinear system identification using Wiener basis functions and perfect sequences

Orcioni

Cecchi

Carini

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Multivariance identification methods exploit input signals with multiple variances for estimating the Volterra kernels of nonlinear systems. They overcome the problem of the locality of the solution, i.e., the fact that the estimated model well approximates the system only at the same input signal variance of the measurement. The estimation of a kernel for a certain input signal variance requires recomputing all lower order kernels. In this paper, a novel multivariance identification method based on Wiener basis functions is proposed to avoid recomputing the lower order kernels with computational saving. Formulas are provided for evaluating the Volterra kernels from the Wiener multivariance kernels. In order to further improve the nonlinear filter estimation, perfect periodic sequences that guarantee the orthogonality of the Wiener basis functions are used for Wiener kernel identification. Simulations and real measurements show that the proposed approach can accurately model nonlinear devices on a wide range of input signal variances.

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A study about Chebyshev nonlinear filters

Cited by 37 publications

References 44 publications

Nonlinear system identification using Wiener basis functions and multiple-variance perfect sequences

Nonlinear system identification using Wiener basis functions and multiple-variance perfect sequences

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

Multivariance nonlinear system identification using Wiener basis functions and perfect sequences

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