On the characterization and reduction of distortion in bandpass filters

Cherry, James A.; Snelgrove, W.M.

doi:10.1109/81.668864

Cited by 21 publications

(15 citation statements)

References 16 publications

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“…where {a s,t p } and {b s,t p } are the scaling function and wavelet filters that appear in the two-scale relationships in Equations (5) and (6). Applied recursively, Equations (35) through (38) can be used to calculate the multiscale coefficients in Equation (34) from the single-scale coefficients in Equation (34).…”

Section: Tensor-product Multiwaveletsmentioning

confidence: 99%

“…They have been employed in a diverse array of engineering applications including the modeling of biological [1,2] and aeroelastic [3][4][5] systems. Volterra filters have been used extensively in the electrical engineering field to compensate for signal distortion from nonlinear disturbances [6,7]. In addition, Volterra models have been used in nonlinear control strategies such as nonlinear model predictive control [8].…”

Section: Introductionmentioning

confidence: 99%

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Multiwavelet Constructions and Volterra Kernel Identification

Prazenica

Kurdila

2006

Nonlinear Dyn

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The Volterra series is commonly used for the modeling of nonlinear dynamical systems. In general, however, a large number of terms are needed to represent Volterra kernels, with the number of required terms increasing exponentially with the order of the kernel. Therefore, reduced-order kernel representations are needed in order to employ the Volterra series in engineering practice. This paper presents an approach whereby multiwavelets are used to obtain low-order estimates of first-, second-, and third-order Volterra kernels. A family of multiwavelets is constructed from the classical finite element basis functions using the technique of intertwining. The resulting multiwavelets are piecewise-polynomial, orthonormal, compactly-supported, and can be constructed with arbitrary approximation order. Furthermore, these multiwavelets are easily adapted to the domains of support of the Volterra kernels. In contrast, most wavelet families do not possess this characteristic. Higher-dimensional multiwavelets can easily be constructed by taking tensor products of the original one-dimensional functions. Therefore, it is straightforward to extend this approach to the representation of higher-order Volterra kernels. This kernel identification algorithm is demonstrated on a prototypical oscillator with a quadratic stiffness nonlinearity. For this system, it is shown that accurate kernel estimates can be obtained in terms of a relatively small number of wavelet coefficients. These results indicate the potential of the multiwavelet-based algorithm for obtaining reduced-order models for a large class of weakly nonlinear systems.

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Section: Tensor-product Multiwaveletsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiwavelet Constructions and Volterra Kernel Identification

Prazenica

Kurdila

2006

Nonlinear Dyn

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“…As a simple example, consider a simple case, where a nonlinear system is driven by a sinusoidal signal (11) Substituting (11) into (2), yields [12], [13] (12) From (12), the input to the th-order submodel contains only one single principal frequency component , the output of the th-order submodel , however, contains many frequency components distributed at . For example, for the linear submodel of the nonlinear system (1), the output frequencies include ; for the 2nd-order nonlinear subsystem, the output frequencies will appear at 0 and .…”

Section: A Description Of Output Frequenciesmentioning

confidence: 99%

“…For a general case, where the input is a summation of multiple sinusoidal waves (13) with , , , , the output of the th-order submodel can be calculated to be [8] …”

Section: A Description Of Output Frequenciesmentioning

confidence: 99%

An Algorithm for Determining the Output Frequency Range of Volterra Models With Multiple Inputs

Wei

Lang

Billings

2007

IEEE Trans. Circuits Syst. II

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. (2007) ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. VOL. 54, NO. 6, JUNE 2007 An Algorithm for Determining the Output Frequency Range of Volterra Models With Multiple Inputs Hua-Liang Wei, Zi-Qiang Lang, and Stephen A. Billings IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-II: EXPRESS BRIEFS,Abstract-A new algorithm for determining the output frequency range and the frequency components of Volterra models under multiple inputs is introduced for nonlinear system analysis. For a given Volterra model, the output frequency components corresponding to a multi-tone input can easily be calculated using the new algorithm.Index Terms-Generalized frequency response functions (GFRF), nonlinear systems, output spectrum, Volterra models.

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“…For instance, we find some applications on reducing amplifiers generated distortion within the transmission set [2][3]. The conditions for Volterra series realization by bilinear systems have been established in [4] and the importance of these systems is based on the fact that they can approximate nonlinear systems behavior with arbitrary precision [5].…”

Section: Introductionmentioning

confidence: 99%

Quadratic System Identification By Hereditary Approach

Etcheverry

Suleiman

Monin

2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings

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Quadratic systems are the first kind of nonlinear systems in which we are interested in order to study polynomial nonlinearities. They can be approximated by bilinear models with nilpotent structure that approximate certain nonlinearities and generate finite degree Volterra series. The hereditary identification algorithm limited until now to linear systems is extended here for identification of nonlinear systems by implementing a canonical structure to the approximant of degree two (quadratic). A NARX (Nonlinear Autoregressive eXogenous input) multidimensional expression is employed in order to perform identification by hereditary computation.

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On the characterization and reduction of distortion in bandpass filters

Cited by 21 publications

References 16 publications

Multiwavelet Constructions and Volterra Kernel Identification

Multiwavelet Constructions and Volterra Kernel Identification

An Algorithm for Determining the Output Frequency Range of Volterra Models With Multiple Inputs

Quadratic System Identification By Hereditary Approach

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