Spectral analysis for non-linear systems, Part I: Parametric non-linear spectral analysis

Billings, S.A.; Tsang, K.M.

doi:10.1016/0888-3270(89)90041-1

Cited by 177 publications

(85 citation statements)

References 12 publications

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“…Moreover, spectral analysis can be performed for nonlinear system through their NARMAX representation by computing the generalised frequency response functions (GFRFs) (Billings and Tsang, 1989a,b, Billings et al, 1990, Chua and Ng, 1979a,b, Jones, 2007, Lee and Chang, 2009, Zhang and Billings, 1993.…”

Section: The Narmax Identification Methodologymentioning

confidence: 99%

Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Florescu¹

2017

Springer Theses

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To my family iii The third problem addressed in this work is given by the need of developing neuromorphic engineering circuits that perform mathematical computations in the spike domain.In this respect, this thesis developed a new representation between the time encoded input and output of a linear filter, where the TEM is represented by an ideal IF neuron. A new practical algorithm is developed based on this representation. The proposed algorithm is significantly faster than the alternative approach, which involves reconstructing the input, simulating the linear filter, and subsequently encoding the resulting output into a spike train.

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Section: The Narmax Identification Methodologymentioning

confidence: 99%

Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Florescu¹

2017

Springer Theses

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“…The probing (or exponential input) method provides a technique for equating Volterra models with models of some other form, M. This allows the nth order FRF, H n , to be described in terms of the parameters of M and hence making the problem more tractable. For models, M, of the NARX class efficient methodologies and algorithms can be found in the literature [32,38,39].…”

Section: Frequency-domain Analysismentioning

confidence: 99%

“…The full derivation is involved and as such is not repeated here. For a thorough description of the mathematical procedure the reader is referred to [23,32].…”

Section: Frequency-domain Analysismentioning

confidence: 99%

“…A key attribute of the framework developed in this investigation is the use of generalised frequency response functions (GFRFs) [32] -for the first time allowing frequency response analysis of nonlinear and time-varying DEA dynamics. The advantage of using GFRFs stems from the fact that the identified NARX model equations are difficult to interpret and directly use for analysis.…”

Section: Introductionmentioning

confidence: 99%

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Control-focused, nonlinear and time-varying modelling of dielectric elastomer actuators with frequency response analysis

Jacobs

Wilson

Assaf

et al. 2015

Smart Mater. Struct.

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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. Control September 2014Abstract. Current models of dielectric elastomer actuators (DEAs) are mostly constrained to first principal descriptions that are not well suited to the application of control design due to their computational complexity. In this work we describe an integrated framework for the identification of control focused, data driven and time-varying DEA models that allow advanced analysis of nonlinear system dynamics in the frequency-domain. Experimentally generated input-output data (voltagedisplacement) was used to identify control-focused, nonlinear and time-varying dynamic models of a set of film-type DEAs. The model description used was the nonlinear autoregressive with exogenous input (NARX) structure. Frequency response analysis of the DEA dynamics was performed using generalised frequency response functions (GFRFs), providing insight and a comparison into the time-varying dynamics across a set of DEA actuators. The results demonstrated that models identified within the presented framework provide a compact and accurate description of the system dynamics. The frequency response analysis revealed variation in the time-varying dynamic behaviour of DEAs fabricated to the same specifications. These results suggest that the modelling and analysis framework presented here is a potentially useful tool for future work in guiding DEA actuator design and fabrication for application domains such as soft robotics.

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“…The theoretical outcome of these nonlinearities can be calculated by conducting a Volterra series of the characteristic, while the usual approximation of those nonlinearities is obtained by conducting a Taylor series. 1,2 Existing methods to study nonlinear behavior of systems are based on transforming the Volterra kernels to the frequency domain to yield the generalized transfer functions. Although these approaches could characterize nonlinear system in the frequency domain properly, the available measurement techniques are all based on extending the classical linear fast Fourier transform algorithms to higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

Harmonics and intermodulation in subthreshold FitzHugh–Nagumo neuron

Wang

Tsang

et al. 2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Intermodulation and harmonics are important in frequency analysis of nonlinear systems. In neuron research, most investigations are taken in studying synchronization between the external stimuli and the output of neuron, but harmonics and intermodulation are often ignored. In this paper, harmonics and intermodulation of the subthreshold FitzHugh-Nagumo neuron are investigated and their magnitudes are used to predict frequency response of the neuron. Furthermore, through analyzing the magnitudes of harmonics, the intrinsic frequencies of the neuron could be identified. A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, while intermodulation is the result of two or more signals of different frequencies being mixed together, forming additional signals at frequencies that are not, in general, at harmonic frequencies of either. Both harmonics and intermodulation are caused by nonlinear behaviors of systems. Recently, they are well investigated in biological applications such as improving human's hearing and vision system. However, in neuron models, harmonics and intermodulation are rarely concerned. Investigators always focus on the external synchronization between the input and output. In traditional study of the external synchronization, signals at continuous frequencies are introduced to stimulate neuron to get corresponding output. By calculating the spectrum or Fourier coefficient of the output at each input frequency, the frequency response is obtained. So harmonics and intermodulation of the applied input signal have been ignored. In this paper, a sinusoid input is applied to FitzHughNagumo (FHN) neuron to make it remain in subthreshold oscillations and the corresponding harmonics and intermodulation are studied. They are incorporated to predict frequency response of the neuron. Also by identifying the maximum magnitude of harmonics, we can get the special input frequencies where the neuron could be more easily excited. Moreover, it demonstrates that the output response of a FHN neuron may not be maximum at the input frequency. Some output frequencies generated from harmonics or intermodulation may have significant effects on the output response which cannot be ignored in frequency analysis of the neuron.

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Spectral analysis for non-linear systems, Part I: Parametric non-linear spectral analysis

Cited by 177 publications

References 12 publications

Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Control-focused, nonlinear and time-varying modelling of dielectric elastomer actuators with frequency response analysis

Harmonics and intermodulation in subthreshold FitzHugh–Nagumo neuron

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