Volterra-series analysis of a class of nonlinear time-varying systems using multilinear parametric transfer functions

Bansal, V.S.

doi:10.1049/piee.1969.0359

Cited by 7 publications

(5 citation statements)

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“…According to the Volterra series theory [9,10], the complex envelope of the output,ỹ k (t), of a non-linear time-varying channel with memory can be written in terms of the complex envelope of the channel input,s k (t), as…”

Section: Time-varying Non-linear Channel With Memorymentioning

confidence: 99%

Performance of mobile orthogonal frequency division multiplexing systems over time‐varying non‐linearities with memory

Hilario-Tacuri

Fortes

2015

IET Communications

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The performance of modern communications transmitters utilising multi-carrier modulation techniques is highly sensitive to non-linear distortions arising mainly from the high-power amplifier. The increase in symbol duration makes the system more sensitive to time-varying channels. In addition, the wideband characteristics of multi-carrier signals result in frequency-dependent distortions, typically known as memory effects. This study presents analytical expressions that can be used to evaluate the impact of the distortions induced by time-varying non-linearities with memory on the bit error rate performance of a multi-carrier signal such as the orthogonal frequency division multiplexing. The timevarying non-linearity with memory is modelled by a time-varying Volterra series. The resulting mathematical expressions are applied to specific situations, allowing for a quantitative evaluation of the system performance degradation.

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Section: Time-varying Non-linear Channel With Memorymentioning

confidence: 99%

Performance of mobile orthogonal frequency division multiplexing systems over time‐varying non‐linearities with memory

Hilario-Tacuri

Fortes

2015

IET Communications

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“…System functions have been extended to non-linear time-varying systems by several authors (Bansal 1969;Yuan and Opal 2001). Consider the time-varying non-linear system which can be expanded in a convergent Volterra series…”

Section: System Functions and Bi-frequency Systemmentioning

confidence: 99%

“…When the parameters change quickly and the speed of change is comparable to the time constants of the system the time variation of the systems cannot be ignored and new methods for time-varying systems are needed. In the past, different representations and techniques have been introduced for the investigation of linear time-varying systems (Zadeh 1950a(Zadeh , 1950bPuri and Weygandt 1963;Wierwille 1963;Kozek and Hlawatsch 1991;Shenoy and Parks 1994;Hlawatsch 1998) and to a much lesser degree non-linear time-varying systems (Bansal 1969;Sandberg 1982;Sandberg 1983;Yuan and Opal 2001). The stability of time-varying systems has also been studied by several authors (Bongiorno 1964;Sandberg 1964;Zames 1966;Brockett and Lee 1967;Zhu and Johnson 1988).…”

Section: Introductionmentioning

confidence: 99%

“…Taking the Fourier transform with respect to the time parameter of the system functions then yields bi-frequency system functions. The bi-frequency system functions have subsequently been developed by Bayan and Erfani (2005), and have been extended to non-linear time-varying cases by some authors (Bansal 1969;Yuan and Opal 2001). Correlation functions and power spectra in variable networks have also been studied (Zadeh 1950a).…”

Section: Introductionmentioning

confidence: 99%

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A parametric frequency response method for non-linear time-varying systems

Guo

Billings

et al. 2013

International Journal of Systems Science

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A new parametric frequency response algorithm is introduced to investigate linear and non-linear dynamic systems with time-varying parameters. In the new algorithm the time-varying parameters are regarded as additional inputs of the systems and the non-linear generalised frequency response functions for multi-input-single-output systems are then employed to obtain Zadeh's system functions from a differential equation representation. The parametric frequency response method reveals how the time-varying parameters affect the behaviour of the systems through a time-varying term. The new method can be applied to both linear and non-linear time-varying systems.

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“…and Bansal (8) have used these transforms to obtain truncated Volterra series solutions to non-linear differential equations associated with systems meeting Brilliant's convergency conditions.…”

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confidence: 99%

Multi-Dimensional Laplace Transforms and Non-Linear Problems

Mullineux

Reed

Richardson

1974

International Journal of Electrical Engineering & Education

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1) IntroductionAs long ago as 1910 an explicit input-output relationship for systems described by a large class of ordinary non-linear differential equations was obtained by Volterra(l) in the form now known as a Volterra series, viz.(1.1) m More recently it has been applied to electrical network and control problems by, amongst others, Wienerv", Barrett'<', Brilliantv", Georgev" and Flake(6). The convergence of this series solution has been discussed by Volterra, Barrett and Brilliant. The last showed that convergence occurred in physical time-invariant systems composed of (a) non-linear subsystems with no memory (i.e. the output of the subsystem depends only on the instantaneous value of the input); (b) linear subsystems with, in general, memory. This class of system is very general and the only excluded class appears to be a hysteretic system. This however leaves open the rate of convergence and for violent non-linearities it could be that a prohibitively large number of terms of the Volterra series would be needed to give an adequate approximation.George'P! explored the use of the Volterra series in the building block approach to control systems and demonstrated the usefulness ofthe multi-dimensional Laplace transform (M.D.L.T.) which can be defined as follows. On introducing a set of artificial time variables t l, t 2, ... , t m into a function x(t) (x(t) == 0 for t < 0) such that x(t) == x(t l, t 2, ... , t m) whenever t = t l = t 2 = ... = t m,The m-dimensional inverse is then given by !l'-I X(SI' S2' ... , sm) = (2 1 .)mf ... f X(SI, S2, ... , sm)exp(sit l + ... + Sm tm> dS I .•. ds.; m 1tJ I, i; (1.3) with tI = t2 = ... = t.. = t and l, the infinite line Res, = c i (a positive constant) > Re(poles ofx treated as a function of S;). at WESTERN MICHIGAN UNIVERSITY on June 5, 2016 ije.sagepub.com Downloaded from

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Volterra-series analysis of a class of nonlinear time-varying systems using multilinear parametric transfer functions

Cited by 7 publications

References 1 publication

Performance of mobile orthogonal frequency division multiplexing systems over time‐varying non‐linearities with memory

Performance of mobile orthogonal frequency division multiplexing systems over time‐varying non‐linearities with memory

A parametric frequency response method for non-linear time-varying systems

Multi-Dimensional Laplace Transforms and Non-Linear Problems

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