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Showing papers on "Volterra series published in 2003"


Book
01 Jan 2003
TL;DR: This book presents a meta-modelling framework for modeling and solving the problems of linear and nonlinear systems through a number of simple and elegant methods.
Abstract: Preface. 1. Introduction. 1.1 Signals. 1.2 Systems and Models. 1.3 System Modeling. 1.4 System Identification. 1.5 How Common are Nonlinear Systems? 2. Background. 2.1 Vectors and Matrices. 2.2 Gaussian Random Variables. 2.3 Correlation Functions. 2.4 Mean-Square Parameter Estimation. 2.5 Polynomials. 2.6 Notes and References. 2.7 Problems. 2.8 Computer Exercises. 3. Models of Linear Systems. 3.1 Linear Systems. 3.2 Nonparametric Models. 3.3 Parametric Models. 3.4 State-Space Models. 3.5 Notes and References. 3.6 Theoretical Problems. 3.7 Computer Exercises. 4. Models of Nonlinear Systems. 4.1 The Volterra Series. 4.2 The Wiener Series. 4.3 Simple Block Structures. 4.4 Parallel Cascades. 4.5 The Wiener-Bose Model. 4.6 Notes and References. 4.7 Theoretical Problems. 4.8 Computer Exercises. 5. Identification of Linear Systems. 5.1 Introduction. 5.2 Nonparametric Time-Domain Models. 5.3 Frequency Response Estimation. 5.4 Parametric Methods. 5.5 Notes and References. 5.6 Computer Exercises. 6. Correlation-Based Methods. 6.1 Methods for Functional Expansions. 6.2 Block Structured Models. 6.3 Problems. 6.4 Computer Exercises. 7. Explicit Least-Squares Methods. 7.1 Introduction. 7.2 The Orthogonal Algorithms. 7.3 Expansion Bases. 7.4 Principal Dynamic Modes. 7.5 Problems. 7.6 Computer Exercises. 8. Iterative Least-Squares Methods. 8.1 Optimization Methods. 8.2 Parallel Cascade Methods. 8.3 Application: Visual Processing in the Light Adapted Fly Retina. 8.4 Problems 8.5 Computer Exercises. References. Index. IEEE Press Series in Biomedical Engineering.

196 citations


Proceedings ArticleDOI
21 Jan 2003
TL;DR: An efficient distortion analysis methodology is presented for analog and RF circuits that utilizes linear-centric circuit models to generate individual distortion contributions due to the various circuit nonlinearities, which provides important design insights regarding the relationships between design parameters and circuit linearity, hence the overall system performance.
Abstract: An efficient distortion analysis methodology is presented for analog and RF circuits that utilizes linear-centric circuit models to generate individual distortion contributions due to the various circuit nonlinearities. The per-nonlinearity distortion results are obtained via a straightforward post-simulation step that is simpler and more efficient than the Volterra series based approaches and do not require the high order device model derivatives. For this reason the order of analysis can be significantly higher than that for a Volterra series implementation while fully accounting for all nonlinearity effects. The proposed methodology is not restricted to weakly nonlinear circuits, but can also analyze per-nonlinearity distortion for active switching mixers and switch capacitor circuits when they are modeled as periodically time-varying weakly nonlinear systems. While Volterra series have also been attempted for this same class of circuits, the requirement of device models for all of the high order model derivatives makes such analysis somewhat impractical. The proposed methodology provides important design insights regarding the relationships between design parameters and circuit linearity, hence the overall system performance. Circuit examples are used to demonstrate the efficacy of the proposed approach, and interesting insights are observed for RF switching mixers in particular.

153 citations


Journal ArticleDOI
TL;DR: In this paper, the variance due to cross-phase modulation and four-wave mixing (FWM) induced intensity distortion is derived based on the Volterra series transfer function method.
Abstract: New analytical tools to calculate the variance due to cross-phase modulation (XPM) and four-wave mixing (FWM) induced intensity distortion are derived based on the Volterra series transfer function method. The analysis for both the XPM and FWM effects is based on the same system configuration with a continuous-wave (CW) probe channel plus modulated pump channels, which makes possible a fair comparison between the two nonlinear effects. Effective ways to reduce the XPM- and FWM-induced intensity distortion are given. The new results on the variance of the nonlinearity-induced intensity fluctuation also make it possible to study both synchronous wavelength-division multiplexing (WDM) systems with fixed channel delays and asynchronous WDM systems with random channel delays. The new analytical results provide accurate and efficient ways for system parameter optimization to reduce these two nonlinear effects.

109 citations


Proceedings ArticleDOI
08 Jun 2003
TL;DR: A novel Volterra-based behavioral model implemented through a bank of parallel FIR filters can reproduce the nonlinear distortion of power amplifiers with memory effects excited by wideband modulated signals with better accuracy compared to conventional quasi-memoryless models.
Abstract: Efficient and accurate behavioral modeling of RF power amplifiers with memory effects becomes of critical importance in the system-level analysis and design of wide band digital communication systems. In this paper, we present a novel Volterra-based behavioral model implemented through a bank of parallel FIR filters, the coefficients of which may be readily extracted from time-domain measurement or circuit envelope simulation. This model can reproduce the nonlinear distortion of power amplifiers with memory effects excited by wideband modulated signals with better accuracy compared to conventional quasi-memoryless models.

108 citations


Journal ArticleDOI
TL;DR: In this paper, the authors reexamine the problem of having non-conservative equations of motion arise from the use of a variational principle and develop a formalism that allows the inclusion of fractional derivatives.
Abstract: We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the Lagrangian framework by treating the action as a Volterra series. It is then possible to derive two equations of motion, one of these is an advanced equation and the other is retarded.

84 citations


BookDOI
23 Jan 2003
TL;DR: In this paper, the authors studied the stability of the solution stability of two-dimensional Volterra Equations of the first kind with two variable integration limits and proved the existence and uniqueness theorem.
Abstract: Introduction Classical Volterra equations of the first kind Classification of integral Volterra equations of the first kind The Gronwall-Bellman lemma A difference analog of the Gronwall-Bellman lemma Self-regularization Two-parametric (a, h)-regularization Inequalities with isotone operators Inequalities with interchangeable isotone operators Unimprovable estimates of solutions of multidimensional integral inequalities The well-posedness of a two-dimensional Volterra Equation of the first kind Unimprovable estimates of solutions for two-dimensional difference inequalities Volterra equations of the first kind with two variable integration limits. The case a(t0) < t0 Problem statement The method of steps Illustrative examples The existence and uniqueness theorem An estimate of the solution stability The study of a special problem of mathematical programming A numerical solution of the test example A geometrical illustration of the reduction by unity in the order of convergence A theorem on the convergence of the quadrature method (the general case) Some numerical results On self-regularization Volterra equations of the first kind with two variable limits of integration. The case a(t0) = t0 Problem statement Solution of the simplest test equation Existence and uniqueness theorem (the general case) Estimation of the solution stability Some generalizations of the Gronwall-Bellman inequality Numerical solution of a test example The proof of convergence for the quadrature method (the general case) Some numerical results Self-regularization (the case of a disturbance in the right-hand side) Stability of a numerical solution with resepect to disturbances of a(t) Multidimensional Volterra equations of the first kind related to the modelling of nonlinear dynamic systems using the Volterra series Bibliography Index

84 citations


Proceedings ArticleDOI
02 Jun 2003
TL;DR: The results indicate that a multiple-point version of NORM can substantially reduce the model size and approach the ultimate model compactness that is achievable for nonlinear system reduction.
Abstract: This paper presents a compact Nonlinear model Order Reduction Method (NORM) that is applicable for time-invariant and time-varying weakly nonlinear systems. NORM is suitable for reducing a class of weakly nonlinear systems that can be well characterized by low order Volterra functional series. Unlike existing projection based reduction methods by J. Roychowdhury et al. (1999), NORM begins with the general matrix-form Volterra nonlinear transfer functions to derive a set of minimum Krylov subspaces for order reduction. Direct moment matching of the nonlinear transfer functions by projection of the original system onto this set of minimum Krylov subspaces leads to a significant reduction of model size. As we will demonstrate as part of our comparison with existing methods, the efficacy of model order for weakly nonlinear systems is determined by the extent to which models can be reduced. Our results further indicate that a multiple-point version of NORM can substantially reduce the model size and approach the ultimate model compactness that is achievable for nonlinear system reduction. We demonstrate the practical utility of NORM for macromodeling weakly nonlinear RF circuits with time-varying behavior.

74 citations


Proceedings ArticleDOI
16 Sep 2003
TL;DR: This work investigates the linearization technique based on terminating the LNA input with low impedance at the low frequencies of the second-order mixing terms and shows it to be very effective in linearizing BJTs but not FETs if the latter are biased in the strong inversion region.
Abstract: This work investigates the linearization technique based on terminating the LNA input with low impedance at the low frequencies of the second-order mixing terms. This technique is analyzed using the Volterra series and is shown to be very effective in linearizing BJTs but not FETs if the latter are biased in the strong inversion region. Several methods to generate the low-frequency low-impedance input termination are reviewed. A SiGe BiCMOS cellular band CDMA LNA using this linearization technique is described. The LNA achieves +11.7dBm IIP3, 15.7dB gain and 1.4dB NF with a current consumption of only 3.9mA@3V.

51 citations


Journal ArticleDOI
TL;DR: In this article, a parametric system identification approach has been adopted in the VOLTERRA series response structure for parameter estimation of polynomial form nonlinearity, where first and higher order frequency response functions are extracted from the measured response harmonic amplitudes through recursive iteration and relationships between higher order FRFs and first order FRF are then employed to estimate the nonlinear parameters.

47 citations


Journal ArticleDOI
TL;DR: In this paper, the generalized frequency-response functions can be applied to interpret systems with subharmonics in the frequency domain, which can then be used to interpret subharmonic generation.
Abstract: Subharmonic generation is a complex nonlinear phenomenon which can arise from nonlinear oscillations, bifurcation and chaos. It is well known that single-input-single-output Volterra series cannot currently be applied to model systems which exhibit subharmonics. A new modeling alternative is introduced in this paper which overcomes these restrictions by using local multiple input single output Volterra models. The generalized frequency-response functions can then be applied to interpret systems with subharmonics in the frequency domain.

38 citations


Journal ArticleDOI
TL;DR: The method is capable of identifying the time-/frequency-domain Volterra kernels/transfer functions of arbitrary causal time-invariant weakly nonlinear circuits and systems operating at high frequencies subject to essentially a general random or multitone excitation.
Abstract: Presents and validates a discrete-time/frequency-domain approach to the problem of Volterra-series-based behavioral modeling for high-frequency systems. The proposed technique is based on the acquisition of samples of the input/output data, both of which are sampled at the Nyquist rate corresponding to the input signal. The method is capable of identifying the time-/frequency-domain Volterra kernels/transfer functions of arbitrary causal time-invariant weakly nonlinear circuits and systems operating at high frequencies subject to essentially a general random or multitone excitation. The validity and efficiency of the proposed modeling approach has been demonstrated by several examples in high-frequency applications and good agreement has been obtained between results calculated using the proposed model and results measured or simulated with commercial simulation tools.

Journal ArticleDOI
TL;DR: An efficient distortion analysis methodology is presented for analog and RF circuits that utilizes linear-centric circuit models to generate individual distortion contributions due to each nonlinear component in a circuit.
Abstract: An efficient distortion analysis methodology is presented for analog and RF circuits that utilizes linear-centric circuit models to generate individual distortion contributions due to each nonlinear component in a circuit. The per-nonlinearity distortion results are obtained via a straightforward post-simulation step that is simpler and more efficient than the Volterra series-based approaches and does not require high-order device-model derivatives. For this reason, the order of analysis can be significantly higher than that for a Volterra series-based implementation while fully accounting for all distortion effects using most existing device models. Moreover, the proposed methodology can also analyze per-nonlinearity distortion for active switching mixers and switch capacitor circuits when they are modeled as periodically time-varying weakly nonlinear systems. The proposed methodology provides important design insights regarding the relationships between design parameters and circuit linearity, hence, the overall system performance. Circuit examples are used to demonstrate the efficacy of the proposed approach, and interesting insights are observed for RF switching mixers in particular.

Journal Article
TL;DR: This paper presents a model for a MEMS variable capacitor (varicap), that can be evaluated much more efficiently and equally accurate during circuit simulation than the differential equations that are normally used to describe this component.
Abstract: Microelectromechanical systems (MEMS) components are gradually finding their way in communication applications. To fully understand their behavior in electrical circuits, an interpretable model is required that, in addition, can be simulated efficiently. This paper presents a model for a MEMS variable capacitor (varicap), that can be evaluated much more efficiently and equally accurate during circuit simulation than the differential equations that are normally used to describe this component. The model, based on Volterra series, describes the frequency dependence (e.g., the mechanical resonance) in combination with the nonlinear behavior of the MEMS varicap. The model is simple enough such that it can be interpreted by designers who want to use the MEMS varicap in RF communication circuits.

Journal ArticleDOI
TL;DR: In this paper, a model for a MEMS variable capacitor (varicap) that can be evaluated much more efficiently and equally accurate during circuit simulation than the differential equations that are normally used to describe this component is presented.
Abstract: Microelectromechanical systems (MEMS) components are gradually finding their way in communication applications. To fully understand their behavior in electrical circuits, an interpretable model is required that, in addition, can be simulated efficiently. This paper presents a model for a MEMS variable capacitor (varicap), that can be evaluated much more efficiently and equally accurate during circuit simulation than the differential equations that are normally used to describe this component. The model, based on Volterra series, describes the frequency dependence (e.g., the mechanical resonance) in combination with the nonlinear behavior of the MEMS varicap. The model is simple enough such that it can be interpreted by designers who want to use the MEMS varicap in RF communication circuits.

Journal ArticleDOI
TL;DR: The main advantage of the proposed technique is that it yields both insight in the nonlinear behavior at the circuit level and that it provides an important gain in simulation efficiency of RF integrated circuits at the system level.
Abstract: The design of analog front-ends of digital telecommunication transceivers requires mixed-signal simulations at the architectural level. The nonlinear nature of the analog front-end blocks is a complication for their modeling at the architectural level, especially when the nonlinear behavior is frequency dependent. This paper describes an analysis and modeling method based on Volterra theory. The method derives bottom-up models of nonlinear analog continuous-time circuits. These behavioral models predict the dominant nonlinear effects using a composition of linear transfer functions and multiplications. This makes it possible to accurately model frequency dependencies and to gain insight into the dominant nonlinear sources of the circuit. The basic models are afterwards described using its multicarrier complex low-pass representation to enable their efficient cosimulation with the digital circuits in a dataflow simulation environment. The multicarrier representation is a direct extension of the classically used complex low-pass equivalent models, which considers the modulation of a single carrier only. The accuracy of the multicarrier representation is higher than classical complex low-pass equivalent models since out-of-band nonlinear distortion is taken into account. The main advantage of the proposed technique is that it yields both insight in the nonlinear behavior at the circuit level and that it provides an important gain in simulation efficiency of RF integrated circuits at the system level. Both aspects are demonstrated on a 5-GHz WLAN design.

Journal ArticleDOI
TL;DR: The electro-thermal Volterra model for calculating third-order intermodulation distortion (IM3) in common emitter (CE) bipolar junction transistor (BJT) RF amplifiers includes nonlinearities caused by input-output cross products, which previous studies have tended to overlook.
Abstract: This transactions brief presents an electro-thermal Volterra model for calculating third-order intermodulation distortion (IM3) in common emitter (CE) bipolar junction transistor (BJT) RF amplifiers. The model includes nonlinearities caused by input-output cross products, which previous studies have tended to overlook, in spite of their significance for RF devices. The nonlinear I-V and Q-V sources of the model are presented also as functions of temperature to analyze how distortion is affected by dynamic temperature variations inside the device. The model is organized to facilitate the recognition of different IM3 components, especially those arising from out-of-band second-order distortion voltages. In addition, this transactions brief presents a technique for characterizing the nonlinearity coefficients of a RF power BJT and studies the behavior of intermodulation distortion as a function of bias point and of out-of-band impedance matching. Optimum bias and matching points are established for the test amplifier, and a good correlation is demonstrated between the calculated and measured data. Finally, this transactions brief shows that some serious memory effects cannot be seen when simulated using the traditional Spice BJT model, but can be detected using the polynomial Volterra model.

Journal ArticleDOI
TL;DR: 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.
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.

Proceedings ArticleDOI
25 May 2003
TL;DR: A 30 W LDMOS is modeled using a 5th order polynomial model and compared to the large-signal MET model using harmonic balance to find out the dominant cause of distortion for a class A biased amplifier.
Abstract: A 30 W LDMOS is modeled using a 5th order polynomial model. The polynomial model is compared to the large-signal MET model using harmonic balance, and as the results agreed very well, the polynomial model was imported to a numerical Volterra simulator to find out the dominant cause of distortion for a class A biased amplifier. The characterization technique is briefly discussed.

Journal ArticleDOI
TL;DR: In this paper, the authors describe different solutions for behavioural identification of non-linear dynamic systems, all based on a modified Volterra series, which is characterized by a reduced number of operators with respect to the classical VOLTERRA approach, allowing a reliable extraction of the model parameters by means of conventional instrumentation, without the need for the generation of complicated input probing signals or additional approximations.

Journal ArticleDOI
TL;DR: The output cumulants up to order 5 are used to determine the Volterra kernels, when the input is a stationary zero mean Gaussian white stochastic process.

Journal ArticleDOI
06 Jun 2003
TL;DR: In this paper, the authors present a new analytical model that describes the nonlinear behaviour of common CMOS operational amplifiers excited by radiofrequency interference (RFI) added to the input nominal signals.
Abstract: The authors present a new analytical model that describes the nonlinear behaviour of common CMOS operational amplifiers excited by radio-frequency interference (RFI) added to the input nominal signals. The new model is a valid support to analogue integrated circuit designers since it expresses a relationship between circuit parameters, parasitic elements and the amplitude of the RFI induced output offset voltage of a feedback CMOS operational amplifier. The validity of model prediction has been verified through a comparison with experimental and computer simulation results.

Journal ArticleDOI
TL;DR: In this paper, a parametric identification procedure based on recursive evaluation of response harmonic amplitude series is presented for a rotor-bearing system supported in rolling element bearings and compared with analytical values and experimental results of previous works.
Abstract: Volterra series provides a structured analytical platform for modeling and identification of nonlinear systems. The series has been widely used in nonparametric identification through higher order frequency response functions or FRFs. A parametric identification procedure based on recursive evaluation of response harmonic amplitude series is presented here. The procedure is experimentally investigated for a rotor-bearing system supported in rolling element bearings. The estimates of nonlinear bearing stiffness obtained from experimentation have been compared with analytical values and experimental results of previous works.

Journal ArticleDOI
TL;DR: In this paper, the system theory of the single-mode laser-diode with electronic feedback is developed and conditions for stability are obtained from the model and stability is dependent on the injection current.

Journal ArticleDOI
TL;DR: A method for verifying that the higher order statistics of the observed time series are matched with the HOS derived from the estimated coefficients, thus proving that the time series is well modeled by the estimated nonlinear parametric model.

Journal ArticleDOI
TL;DR: A nonlinear dynamic "black box" model for sample-hold and analogue to digital conversion devices (S/H-ADCs) is proposed, based on a discrete convolution in the time domain, which describes the nonlinear dynamics of the system.

Journal ArticleDOI
TL;DR: In this article, a proper decomposition of experimental chaotic flow fields, followed by a projection of the complex Ginzburg-Landau equation (CGLE) onto the proper directions is used to reconstruct the spatio-temporal chaos observed in the experiment.

Proceedings ArticleDOI
02 Jun 2003
TL;DR: While the macromodel can trade accuracy for simplicity in terms of the number of frequency expansion points, it is found that expansion about one frequency point provides the accuracy required for system-level analysis of most RF and narrow-band analog components.
Abstract: Design and validation of mixed-signal integrated systems require system-level model abstractions. Generalized Volterra series based models have been successfully applied for analog and RF component macromodels, but their complexity can sometimes limit their utility for time-varying systems and large circuits with complex device models or numerous parasitics. In this paper we propose simple and efficient analog and RF circuit macromodels that provide accurate model abstractions for large, complex time-varying circuits over frequency bands of interest. By starting with the system-level block diagram model structures and focusing on the narrow RF bands, the proposed macromodels can efficiently capture the nonlinear behavior as well as the impact of RLC coupling parasitics via compact reduced-order model forms. While the macromodel can trade accuracy for simplicity in terms of the number of frequency expansion points, we find that expansion about one frequency point provides the accuracy required for system-level analysis of most RF and narrow-band analog components. The macromodel form corresponds to block diagram structures that are easily incorporated into our system-level simulation tool based on Simulink.

Journal ArticleDOI
TL;DR: In this article, a technique based on statistical quadratization and cubicization is proposed to determine the stationary response of a nonlinear system with a polynomial nonlinearity of either quadratic or cubic order, which can be solved by the Volterra series method.
Abstract: Random vibrations of nonlinear systems subjected to Gaussian input are investigated by a technique based on statistical quadratization, and cubicization. In this context, and depending on the nature of the given nonlinearity, statistics of the stationary response are obtained via an equivalent system with a polynomial nonlinearity of either quadratic or cubic order, which can be solved by the Volterra series method. The Volterra series response is expanded in a trigonometric Fourier series over an adequately long interval T, and exact expressions are derived for the Fourier coefficients of the second- and third-order response in terms of the Fourier coefficients of the first-order, Gaussian response. By using these expressions, statistics of the response are determined using the statistics of the Fourier coefficients of the first-order response, which can be readily computed since these coefficients are independent zero-mean Gaussian variables. In this manner, a significant reduction of the computational cost is achieved, as compared to alternative formulations of quadratization and cubicization methods where rather prohibitive multifold integrals in the frequency domain must be determined. Illustrative examples demonstrate the reliability of the proposed technique by comparison with data from pertinent Monte Carlo simulations.

Journal ArticleDOI
TL;DR: An approach to estimate the distortion in log-domain filters is presented, using models used for the bipolar transistors, the beta effect, and the parasitic emitter resistances.
Abstract: An approach to estimate the distortion in log-domain filters is presented. The models used for the bipolar transistors include the C/sub /spl pi// and C/sub sub/ parasitic capacitors, the beta effect, and the parasitic emitter resistances. Simple closed-form expressions describing the effect of each nonideality on distortion are derived and compared to simulations. A general method, which could be extended to analyze higher order filters, based on Volterra series, is used.

Journal ArticleDOI
TL;DR: This paper addresses a Volterra series representation of bilinear (or quadratic) time-frequency distributions that belong to Cohen's class, whereby the analogy of the bil inear class with a second-order double VolterRA series is utilized.
Abstract: This paper addresses a Volterra series representation of bilinear (or quadratic) time-frequency distributions that belong to Cohen's class, whereby the analogy of the bilinear class with a second-order double Volterra series is utilized. In addition, a different viewpoint for the bilinear kernel and a complementary interpretation concerning the quadratic time-frequency distributions are provided.