A modified Volterra series approach for nonlinear dynamic systems modeling

Mirri, D.; Luculano, G.; Filicori, F.; Pasini, G.; Vannini, G.; Gabriella, G.P.

doi:10.1109/tcsi.2002.801239

Cited by 98 publications

(59 citation statements)

References 15 publications

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“…On the other hand, the Volterra series representation is usually considered to be more effective but less practical due to the highly complex calculation of multidimensional kernels [30][31][32][33]. A Generalized Hammerstein model [16][17][18] represents a very good compromise between the complexity and the efficacy.…”

Section: Nonlinear Modelsmentioning

confidence: 99%

Measurements and Modeling of the Nonlinear Behavior of a Guitar Pickup at Low Frequencies †

et al. 2017

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Description of the physical behavior of electric guitars is still not very widespread in the scientific literature. In particular, the physical models describing a nonlinear behavior of pickups still requires some refinements. The study presented in this paper is focused on nonlinear modeling of the pickups. Two main issues are raised. First, is the currently most used nonlinear model (a Hammerstein model) sufficient for the complex nonlinear behavior of the pickup? In other words, would a more complex model, such as a Generalized Hammerstein that can deal better with the nonlinear memory, yield better results? The second troublesome issue is how to measure the nonlinear behavior of a pickup correctly. A specific experimental set-up allowing for driving the pickup in a controlled way (string displacement perpendicular to the pickup) and to separate the nonlinear model of the pickup from other nonlinearities in the measurement chain is proposed. Thanks to this experimental set-up, a Generalized Hammerstein model of the pickup is estimated for frequency range 15-500 Hz and the results are compared with a simple Hammerstein model. A comparison with experimental results shows that both models succeed in describing the pickup when used in realistic conditions.

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Section: Nonlinear Modelsmentioning

confidence: 99%

Measurements and Modeling of the Nonlinear Behavior of a Guitar Pickup at Low Frequencies †

et al. 2017

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“…Since these circuits appear strongly nonlinear in voltage but are almost linear (i.e. weakly nonlinear) in the selected variable domains, it makes sense to model the circuit first as a weakly-nonlinear system in the selected variables, based on various weakly-nonlinear models described in [13][14][15][16], and then convert it to a voltage-domain model using the translators. Note that modeling the circuits directly as strongly-nonlinear systems is very difficult and only a few limited methods are known to date [17,18].…”

Section: Variable Domain Translatorsmentioning

confidence: 99%

“…Figure 2(b) illustrates converting a phase-domain macromodel of a PLL to a voltage-domain model using the voltage-to-phase and phase-tovoltage translators. The phase-domain macromodel can be generated algorithmically from the phase-domain pseudo-circuit in Figure 2(a) [13,[15][16][17][18]], but we found the modified Volterra series approach outlined in [14] particularly suitable to generate the macromodels from the PSS and PAC simulation results.…”

Section: Variable Domain Translatorsmentioning

confidence: 99%

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Variable domain transformation for linear PAC analysis of mixed-signal systems

Kim

Jones

Horowitz

2007

2007 IEEE/ACM International Conference on Computer-Aided Design

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent repository link ABSTRACTThis paper describes a method to perform linear AC analysis on mixed-signal systems which appear strongly nonlinear in the voltage domain but are linear in other variable domains. Common circuits like phase/delay-locked loops and duty-cycle correctors fall into this category, since they are designed to be linear with respect to phases, delays, and duty-cycles of the input and output clocks, respectively. The method uses variable domain translators to change the variables to which the AC perturbation is applied and from which the AC response is measured. By utilizing the efficient periodic AC (PAC) analysis available in commercial RF simulators, the circuit's linear transfer function in the desired variable domain can be characterized without relying on extensive transient simulations. Furthermore, the variable domain translators enable the circuits to be macromodeled as weakly-nonlinear systems in the chosen domain and then converted to voltagedomain models, instead of being modeled as strongly-nonlinear systems directly.

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“…Finally, kernel measurement techniques are often based on recursive algorithms, whose results can strongly suffer from relevant errors due to experimental data uncertainty propagation. In order to overcome such limitations, the authors previously proposed a "modified" Volterra series [5] which, besides preserving the same generality and theoretical validity of the classical approach, 1 can be practically applied also in presence of strong nonlinearities (if mild hypotheses on the duration of system memory time are satisfied) or, when the nonlinear effects are weak, associated with a simple experimental procedure based on conventional measurements and reliable algorithms. Sample/hold (S/H) and analog-to-digital conversion (ADC) device modeling represents an interesting application of the modified series, which allows characterization of not only static, but also dynamic nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

A non-linear dynamic S/H-ADC device model based on a modified Volterra series: identification procedure and commercial CAD tool implementation

Traverso

Mirri²,

Pasini³

et al.

IMTC/2002. Proceedings of the 19th IEEE Instrumentation and Measurement Technology Conference (IEEE Cat. No.00CH37276)

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Abstract-A nonlinear, dynamic empirical model, based on a Volterra-like approach, was previously proposed by the authors for the time-oriented characterization of sample/hold (S/H) and analog-to-digital conversion (ADC) devices. In this paper, the experimental procedure for model parameter measurement is presented, as well as techniques devoted to the implementation of the model in the framework of the main commercial CAD tools for circuit analysis and design. Examples of simulations, performed both in the time and frequency domain on the model obtained for a commercial device, are proposed, which show the model's capability of pointing out the dynamic nonlinear effects in the S/H-ADC response.Index Terms-Analog-to-digital conversion (ADC) modeling, ADC converter, nonlinear dynamic model, nonlinear dynamic system, sample-hold (S/H), Volterra series.

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A modified Volterra series approach for nonlinear dynamic systems modeling

Cited by 98 publications

References 15 publications

Measurements and Modeling of the Nonlinear Behavior of a Guitar Pickup at Low Frequencies †

Measurements and Modeling of the Nonlinear Behavior of a Guitar Pickup at Low Frequencies †

Variable domain transformation for linear PAC analysis of mixed-signal systems

A non-linear dynamic S/H-ADC device model based on a modified Volterra series: identification procedure and commercial CAD tool implementation

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