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Showing papers on "Volterra series published in 1989"


Journal ArticleDOI
TL;DR: The quick method to measure directly the points of the Volterra kernels which are located along one or more axes in the frequency domain is developed, thus making the method complete and more accurate than that presented in Reference 1.
Abstract: Accurate measurement of Volterra kernels is an essential step in the modelling of weakly non-linear physical systems via the block box approach, and in model validation. This paper is a sequel to an earlier paper,1 where practical methods for measuring Volterra kernels were presented along with a quick method for measuring the second-order Volterra kernels. This paper extends that quick method for measuring higher-order frequency-domain Volterra kernels of weakly non-linear systems. We further developed the quick method to measure directly the points of the Volterra kernels which are located along one or more axes in the frequency domain, thus making our method complete and more accurate than that presented in Reference 1. We illustrate our method by actually measuring a weakly non-linear circuit whose Volterra kernels can be accurately calculated. the experimentally measured and the theoretically predicted results agree remarkably well.

96 citations


Journal ArticleDOI
TL;DR: The sensitivity of the IM intercept point (IP/sub 3/) to the source-reflection coefficient, Gamma /sub s/, is shown to decrease with increasing frequency and is related to the MESFET's stability.
Abstract: It is shown how the intermodulation (IM) distortion performance of a small-signal amplifier can be optimized when the amplifier is designed according to available-gain criteria. In this process the MESFET's output is conjugate-matched and its input is mismatched to obtain a specified gain. This method generally results in a better dynamic range than obtained with other options such as matching the input and mismatching the output or simultaneously matching both the input and output (which, in many cases, is impossible). In available-gain design the value of source impedance that provides the desired gain is not unique and can be selected to optimize IM levels. A numerical formulation of the Volterra series allows a complete equivalent circuit of the FET to be used, and the intermodulation calculations include all feedback effects. The sensitivity of the IM intercept point (IP/sub 3/) to the source-reflection coefficient, Gamma /sub s/, is shown to decrease with increasing frequency and is related to the MESFET's stability. >

60 citations


Journal ArticleDOI
TL;DR: In this paper, a novel approach for determining the amplitude and frequency of nonlinear FET oscillators is presented, where the nonlinear elements of the active device are modeled by the Volterra series method and the frequency and amplitude of oscillation are calculated by solving two algebraic equations.
Abstract: A novel approach for determining the amplitude and frequency of nonlinear FET oscillators is presented. The nonlinear elements of the active device are modeled by the Volterra series method. The frequency and amplitude of oscillation are then calculated by solving two algebraic equations. Experimental results obtained from a constructed oscillator confirm the validity of the theory, the discrepancy between measured and calculated frequency and amplitude values being less than 10%. >

38 citations


01 Jul 1989
TL;DR: In this paper, a computer program is described that performs a Volterra-series analysis of a weakly nonlinear microwave circuit having an arbitrary topology, using the method of nonlinear currents and a nodal formulation.
Abstract: A computer program is described that performs a Volterra-series analysis of a weakly nonlinear microwave circuit having an arbitrary topology. The program uses the method of nonlinear currents and a nodal formulation. In this approach, each nonlinear circuit element is described as a linear element in parallel with a set of current sources; each current source represents a single order (greater than one) of the mixing products, and its current is a nonlinear function of the node-voltage components at lower-order mixing frequencies. The weakly nonlinear circuit is reduced to a linear circuit, which contains the linear elements and the linear parts of the nonlinear elements, and a set of excitation sources. The program is intended primarily for use in the design of microwave circuits; its catalog of circuit elements includes the distributed elements necessary for such work. Because the program formulates and solves the circuit equations numerically, the user need not simplify either the circuit or the model of the solid-state device, or make any of the other common simplifying assumptions. >

38 citations


Journal ArticleDOI
TL;DR: It is pointed out that while the Volterra kernels can easily be derived from the block-oriented models, the structure and the parameters cannot be computed in a trivial way from the estimated VolterRA kernels.
Abstract: Block-oriented models having only one multiplier and the Volterra kernels that describe them are summarized. The kernel estimation of the discrete Volterra series is dealt with. It is pointed out that while the Volterra kernels can easily be derived from the block-oriented models, the structure and the parameters of the block-oriented models cannot be computed in a trivial way from the estimated Volterra kernels. Both graphical and analytical procedures are recommended for the structural identification. The method is supported by several simulation examples.

21 citations


Proceedings ArticleDOI
23 May 1989
TL;DR: To sufficiently reduce the nonlinearities caused by A/D and D/A (analog/digital and digital/analog) converters, an adaptive third-order Volterra filter with a nonlinear memory of length three can be applied.
Abstract: A nonlinear echo canceller with Volterra series expansion is presented. A model of the data transmission system is used to study its performance. It is shown that the Volterra expansion method is a good solution to the problem of nonlinear echo cancellation. To sufficiently reduce the nonlinearities caused by A/D and D/A (analog/digital and digital/analog) converters, an adaptive third-order Volterra filter with a nonlinear memory of length three can be applied. The far-end signal has a very strong influence on the canceller. To reduce this, a training sequence without a far-end signal is used, and different values of the step-size mu are chosen for the transient period (larger mu ) and for the steady state. Simulations have shown that the canceller can achieve 15-dB improvement with a training sequence and 8-dB improvement without the training sequence. >

19 citations


Dissertation
01 Jan 1989

18 citations


Proceedings ArticleDOI
08 May 1989
TL;DR: In this paper, the effects caused by weak nonlinearities of operational transconductance amplifiers (OTAs) on the performance of continuous-time OTA-capacitor (TAC) filters are investigated.
Abstract: Effects caused by weak nonlinearities of operational transconductance amplifiers (OTAs) on the performance of continuous-time OTA-capacitor (TAC) filters are investigated. Nonlinear phenomena, such as compression/expansion and desensitization, and their effects on the frequency responses of TAC filters are discussed. The Volterra series method is used to represent filters by their nonlinear transfer functions for steady-state analysis and simulation. Using this approach, distortion and interference criteria are given for analytically predicting the onset of nonlinear behavior and for establishing appropriate design guidelines. Representative simulation results are included. >

10 citations


Proceedings ArticleDOI
13 Jun 1989
TL;DR: In this paper, a novel analytical technique is described based on generalized Volterra series to analyze nonlinear microwave and millimeter-wave circuits and devices, which is especially efficient for general-purpose CAD (computer-aided design) applications and can be easily incorporated into existing CAD programs.
Abstract: A novel analytical technique is described based on generalized Volterra series to analyze nonlinear microwave and millimeter-wave circuits and devices. This method is especially efficient for general-purpose CAD (computer-aided design) applications and can be easily incorporated into existing CAD programs. Nonlinear S parameters can be defined using this technique to accurately predict circuit performance or device S parameters at the onset of large-signal excitation. The capabilities of the technique have been demonstrated on MESFET structures, designed to reduce the losses due to the high resistance of the gate electrode. Power and intermodulation distortion measurements have been carried out and good agreement with calculated values has been observed. >

6 citations


Journal ArticleDOI
TL;DR: In this paper, a symbolic transform that generalizes Laplace transform of signals depend only on the time of the generating series is obtained, and the Taylor expansion of triangular Volterra kernels is deduced.

5 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that a large class of maps that have Volterra series representations also have these representations, which are called g-and h-representations, for important classes of systems governed by nonlinear integral equations.
Abstract: Examples are given concerning the range of applicability of recent representation results that provide a means of studying the input-output properties of nonlinear systems in terms of the familiar impulse-response concept, and which extend the concept of integral transformation to nonlinear maps. We show that such representations, which we call “g-” and “h-representations,” exist for important classes of systems governed by nonlinear integral equations. In particular, it is proved that a large class of maps that have Volterra series representations also have these representations.

Journal ArticleDOI
TL;DR: This work examines conditions on the Volterra kernels that determine if the system is in some sense equivalent to a linear system, and relates theVolterra series description of a feedback linearizable system to its state-space description.
Abstract: Given the Volterra series representation of a single input, single output nonlinear system, we examine conditions on the Volterra kernels that determine if the system is in some sense equivalent to a linear system. The systems considered herein are known as “feedback linearizable” systems. Feedback linearizable systems are usually discussed in terms of their state-space representations. A key result relates the Volterra series description of a feedback linearizable system to its state-space description.

Proceedings ArticleDOI
23 May 1989
TL;DR: Given a Volterra series representation of an input-output system, the authors present a result concerning conditions under which there exists a feedback linearizable realization of the nonlinear system and develop a method to compute the unknown parameters in a canonical-form realization from the known VolterRA kernels.
Abstract: Given a Volterra series representation of an input-output system, the authors present a result concerning conditions under which there exists a feedback linearizable realization of the nonlinear system. In addition, they develop a method to compute the unknown parameters in a canonical-form realization from the known Volterra kernels. A finite number of parameters can be calculated from an associated finite number of the kernels. >

Journal ArticleDOI
TL;DR: The letter presents a quasitriangular semisystolic array for the implementation of nonlinear second-order Volterra digital filters based on the recurrence algorithm of Volterro filtering, which is derived here.
Abstract: The letter presents a quasitriangular semisystolic array for the implementation of nonlinear second-order Volterra digital filters. The performance of the proposed systolic array is based on the recurrence algorithm of Volterra filtering, which is also derived here.

01 Jan 1989
TL;DR: The implemented network's ability to perform contrast enhancement, data compression, and adaptation to mean input strength level, as well as its tunability of sensitivity, are well-suited for processing of sensory information in general and visual information in particular.
Abstract: A framework for extremely compact, all analog, and massively parallel implementation of shunting recurrent and nonrecurrent neural networks that is applicable to a wide variety of FET-based integration technologies is proposed. A specific circuit designed for implementation with gallium arsenide MESFETs is implemented. The implemented network's ability to perform contrast enhancement, data compression, and adaptation to mean input strength level, as well as its tunability of sensitivity, are well-suited for processing of sensory information in general and visual information in particular. Thus, if integrated with an array of photo-detectors, it can find widespread optoelectronics applications. These properties are also desirable for feature extraction for content addressable memory (CAM) systems. Furthermore, the network fits in self-organizing multilayer network architectures of Adaptive Resonance Theory. The asymptotic global stability of the network is shown by finding a global Liapunov energy function, which serves to show that the network itself is capable of CAM. The time trace of the local activity of the implemented network is found via a variational analysis which leads to the identification of higher order kernels in a Volterra series expansion. The same mathematical techniques are applied to find higher order spatial kernels which explains the extraordinary high order classification properties embedded in simple multiplicative nonlinearity.

Proceedings Article
05 Sep 1989
TL;DR: In this article, the region of convergence of Volterra series describing continuous-time lowpass filters based on OTA-C integrators has been considered for low frequency signals.
Abstract: The region of convergence of Volterra series describing continuous-time lowpass filters based on OTA-C integrators has been considered. Firstly the filter containing one OTA-C integrator has been studied. In this case for low frequency signals the Volterra series is an ordinary power series with an appointed radius of convergence. In a more general case when the circuits containing more than one nonlinear element for continuous and bounded input signals, one can only determine sufficient conditions for which the Volterra series is convergent. In particular, simple conditions of convergence for lowpass second-order OTA-C filters are presented. Using known numerical methods for computing the solution of the nonlinear equation, the size of the region of convergence can be determined more exactly. The method developed here is applied to determine the amplitude of an input harmonic signal for typical values of parameters.

30 Sep 1989
TL;DR: In this article, the dependence of third-order intermodulation distortion on the source reflection coefficient Gamma sub s as a function of frequency, in an amplifier designed according to available-gain criteria is examined.
Abstract: : This report examines the dependence of third-order intermodulation distortion on the source reflection coefficient Gamma sub s as a function of frequency, in an amplifier designed according to available-gain criteria By means of a numerical formulation of the Volterra series, a complete equivalent circuit of the FET can be used, and intermodulation calculations include all feedback effects The sensitivity of IP3 to Gamma sub s decreases with increasing frequency and can be related to the MESFET's stability Keywords: Intermodulation distortion; Nonlinear distortion; Volterra series; Field effect transistor amplifier

Book ChapterDOI
01 Jan 1989
TL;DR: In this article, the authors describe representations of the input-output behavior of a nonlinear system in terms of input and output representations of nonlinear systems, and the purpose of this section and of the following one is to describe the representation of the inputs and outputs of the system.
Abstract: The purpose of this section and of the following one is to describe representations of the input-output behavior of a nonlinear system.

Journal ArticleDOI
TL;DR: In this paper, a methode for l'identification ou l'approximation de systemes avec des signaux de test discrets, est etablie.
Abstract: Une methode pour l'identification ou l'approximation de systemes avec des signaux de test discrets, est etablie. L'identification non lineaire par excitation de bruit aleatoire est examinee aussi

Journal ArticleDOI
TL;DR: In this article, a generalized frequency response is proposed for an input-output map. And a realization theory is developed and the generalized frequency response (GRF) is presented for a special case of the Volterra series, and a simple example is given that the new representations have improved convergence properties.
Abstract: A realization theory is developed and the ‘generalized frequency response’ is presented for an input-output map introduced in a previous work. Relations with the realization of finite Volterra series are outlined. A simple example is given to show that the new representations have improved convergence properties.

Journal ArticleDOI
TL;DR: In this paper, a method of computing approximations of periodic solutions is presented, using harmonic balancing based on the Volterra input output description, from which the approximate frequency and amplitudes of a suitable number of harmonics can be determined.

01 Jan 1989
TL;DR: In this article, the feasibility of the time invariant nonlinear (weakly) system transfer function estimation and identification is considered and a mathematical framework is laid out in terms of the Volterra series.
Abstract: The theoretical aspects and mathematical framework towards the feasibility of the time invariant nonlinear (weakly) system transfer function estimation and identification are considered A mathematical framework is laid out in terms of the Volterra series This approach attempts to circumvent conventional problems in identifying the nonlinear set of parameters that renders the Volterra series attractive to nonlinear systems but ackward to apply Since an unknown TIV system is presumed for an observed output of some known input, measures applied for system linearity provide a handle to identifying the existence of a nonlinear system The methodology outlined provides an estimate of nonlinear system parameters such as to become useful in unknown communication channels which could be categorized by their particular nonlinear characteristic outputs Such an approach would facilitate a prior knowledge for identification of linear versus nonlinear channels, including differentiation between those identified as being nonlinear

Proceedings ArticleDOI
01 Jan 1989
TL;DR: In this paper, a mathematical framework for nonlinear transfer function estimation and identification is presented, in terms of the Volterra series, which can be used to identify the nonlinear set of parameters that renders the VOLTERRA series attractive to nonlinear systems but awkward to apply.
Abstract: The theoretical aspects and mathematical framework of the time-invariant (TIV) nonlinear (weakly) system transfer function estimation and identification are considered to determine their feasibility. A mathematical framework is laid out in terms of the Volterra series. The approach attempts to circumvent conventional problems in identifying the nonlinear set of parameters that renders the Volterra series attractive to nonlinear systems but awkward to apply. Since an unknown TIV system is presumed for an observed output of some known input, measures applied for system linearity provide a means for identifying the existence of a nonlinear system. The methodology outlined provides an estimate of nonlinear system parameters that is useful in unknown communication channels which can be categorized by their particular nonlinear characteristic outputs. Such an approach facilitates identification of linear versus nonlinear channels, including differentiation between those identified as being nonlinear. >

Proceedings ArticleDOI
13 Dec 1989
TL;DR: In this article, the authors give necessary conditions for the optimality of totally and partially singular arcs in the case of nonlinear systems not necessarily linear in the control variables, where the necessary conditions are expressed in terms of the derivative of a particular function along suitable Lie brackets involving vector fields associated with the control process.
Abstract: High order necessary conditions are given for the optimality of totally and partially singular arcs in the case of nonlinear systems not necessarily linear in the control variables. The term 'singular' is used in optimal control problems in which the Pontryagin maximum principle does not furnish in explicit relationship between the control and the state and costate variables. Singular arcs rise in practical applications in rocket and air vehicle flight, and many techniques have been used. In the present study these results are unified and third and higher order necessary conditions are obtained. The necessary conditions are all expressed in terms of the derivative of a particular function along suitable Lie brackets involving vector fields associated with the control process. It is shown that there is a rich interplay between the Lie bracket structure of a system and the qualitative properties of external controls. The result is a key tool in that it provides some suitable control variations in the proof of the theorems. The remaining results are proved by combining Volterra series expansions, special control variations, and multiple integral identities. >

Journal ArticleDOI
TL;DR: The method of measuring the kernels, where an arbitrary set of orthonormal functions can be taken without the assumption that the input is white, is presented by applying Karhunen-Loeve expansion theorem.
Abstract: The measurement of the kernels of the Volterra series model of a nonlinear system is generally carried out as follows; first a parametric model is derived by applying orthogonal expansions to the kernels, and then the parameters are optimally determined in the sense of the least mean square error of the input/output experiments of the system. In this method, if the input is a white Gaussian signal, the amount of computation required is greatly reduced whenever an arbitrary set of orthonormal functions is used for the expansion of the kernels. On the other hand, if the input is a stationary nonwhite Gaussian signal, the set of orthonormal functions cannot be taken arbitrarily for the purpose of computational reduction. In this paper, the method of measuring the kernels, where an arbitrary set of orthonormal functions can be taken without the assumption that the input is white, is presented by applying Karhunen-Loeve expansion theorem. The key of the present method is that a nonstationary Gaussian random process is generated from an arbitrary set of orthonormal functions used for the expansion of the kernels and a set of uncorrelated Gaussian random variables, and it is used as the input.

Proceedings ArticleDOI
09 Nov 1989
TL;DR: This work uses the algorithm of S.Y. Fakhouri (1980) to produce kernel identification of volterra series of the thermoregulatory control system and contains the linear part (first-order kernel) in parallel.
Abstract: The modeling and identification of the thermoregulatory control system is considered, relating the thermal stimulus as input and heart rate variability as output of the system The thermal stimulus is produced by using an entrainment device that is designed to provide hot and cold air at different frequencies covering the range of 85 to 805 (00125 to 0125 Hz) This stimulus is directed by the entrainment device to the arm or leg through a plastic sheath for a period of 10 min The thermal input as well as the heart rate variability signals as output are recorded by using power spectrum analysis This work uses the algorithm of SY Fakhouri (1980) to produce kernel identification of volterra series of the system The model contains the linear part (first-order kernel) in parallel >

Proceedings ArticleDOI
V. Raman1, R. Liu
13 Dec 1989
TL;DR: In this paper, the existence of Volterra series representations for transfer operators is proved in an operator-theoretic framework that is shown to result from the system-theory problem under appropriate conditions.
Abstract: The design of a nonlinear feedback system that guarantees the existence of Volterra series representations for (transfer) operators is important for preserving the nonchaotic behavior of the system. Necessary and sufficient conditions for the existence of such operators are shown. The controller parameterization is not restrictive of the parameter. This result is demonstrated in an operator-theoretic framework that is shown to result from the system-theoretic problem under appropriate conditions. >

30 Sep 1989
TL;DR: In this paper, the third-order intermodulation distortion of small-signal MESFET amplifiers, subject to available-gain criteria, is derived. And the sensitivity of IP(3) to gamma (s) decreased with frequency and can be related to the MES-FET's stability.
Abstract: : Matching conditions that optimize the third-order intermodulation distortion of small-signal MESFET amplifiers, subject to available-gain criteria, are derived. A numerical formulation of the Volterra series is used in conjunction with a complete equivalent circuit of the FET. The sensitivity of IP(3) to gamma (s) decreased with frequency and can be related to the MESFET's stability. (RRH)

Proceedings ArticleDOI
09 Nov 1989
TL;DR: The auditory system is represented by a third-order Volterra series, and the cross-section function resulting from applying theCross-correlation method with an m pulse sequence as the input is derived in terms ofVolterra kernels.
Abstract: The auditory system is represented by a third-order Volterra series, and the cross-section function resulting from applying the cross-correlation method with an m pulse sequence as the input is derived in terms of Volterra kernels. The function can be used to predict system responses to pulse trains of different pulse rates. It is therefore concluded that the m pulse sequence may be an effective and efficient stimulus for studying nonlinear rate effects in neurological systems. >