Showing papers on "Volterra series published in 1999"

Effect of out-of-band terminations on intermodulation distortion in common-emitter circuits

Abstract: This paper presents the results of Volterra series analysis of the third-order intermodulation distortion in common-emitter circuits. The derived closed-form expression shows how out-of-band source and load impedances affect the distortion. The expression was used to optimally tune the input matching network of a 2 GHz Si BJT LNA at the sub- and second-harmonic frequencies for a higher IIP/sub 3/. While the in-band noise figure, gain and input return loss were not affected, the peak IIP/sub 3/ increased by 14 dB.

High-frequency distortion analysis of analog integrated circuits

Abstract: An approach is presented for the analysis of the nonlinear behavior of analog integrated circuits. The approach is based on a variant of the Volterra series approach for frequency domain analysis of weakly nonlinear circuits with one input port, such as amplifiers, and with more than one input port, such as analog mixers and multipliers. By coupling numerical results with symbolic results, both obtained with this method, insight into the nonlinear operation of analog integrated circuits can be gained. For accurate distortion computations, the accuracy of the transistor models is critical. A MOS transistor model is discussed that allows us to explain the measured fourth-order nonlinear behavior of a 1 GHz CMOS upconverter. Further, the method is illustrated with several examples, including the analysis of an operational amplifier up to its gain-bandwidth product. This example has also been verified experimentally.

Distortion analysis of MOS track-and-hold sampling mixers using time-varying Volterra series

Abstract: A time-varying theory of Volterra series is developed and applied in the sampled-data domain to solve for harmonic and intermodulation distortion of a MOS-based track-and-hold sampling mixer with a nonzero fall-time LO waveform. Distortion due to sampling error is also calculated. These results, when combined with the continuous-time solution, quantify harmonic and intermodulation distortion of a track-and-hold type mixer completely. Closed form solutions are obtained. As a practical consequence, it is shown that for certain fall-time, the distortion of track-and-hold mixers can be better than what would be predicted by a simple application of time-invariant Volterra series theory.

Modeling of nonlinear nonstationary dynamic systems with a novel class of artificial neural networks

Abstract: This paper introduces a novel neural-network architecture that can be used to model time varying Volterra systems from input-output data. The Volterra systems constitute a very broad class of stable nonlinear dynamic systems that can be extended to cover nonstationary (time-varying) cases. This novel architecture is composed of parallel subnets of three-layer perceptrons with polynomial activation functions, with the output of each subnet modulated by an appropriate time function that gives the summative output its time-varying characteristics. The paper shows the equivalence between this network architecture and the class of time-varying Volterra systems, and demonstrates the range of applicability of this approach with computer-simulated examples and real data. Although certain types of nonstationarities may not be amenable to this approach, it is hoped that this methodology will provide the practical tools for modeling some broad classes of nonlinear, nonstationary systems from input-output data, thus advancing the state of the art in a problem area that is widely viewed as a daunting challenge.

Genetic algorithm based identification of nonlinear systems by sparse Volterra filters

Abstract: A parsimonious parameterization scheme is proposed to model the sparse Volterra filter so that the number of Volterra kernels to be estimated is greatly reduced. Representing the Volterra filter using a linear vector equation, the genetic algorithm is applied to search the significant terms among all possible candidate vectors. As the significant terms are detected, the associated Volterra kernels are estimated using the least square error method. The problem to be solved is, in essence, the application of the genetic algorithm to combinatorial optimization. An operator called forced mutation is proposed along with the genetic algorithm to overcome the difficulties usually encountered when applying the genetic algorithm to combinatorial optimization.

A frequency-domain, Volterra series-based behavioral simulation tool for RF systems

Abstract: In this paper a new behavioral modeling approach for RF systems based is presented, based on a Volterra series input-output map representation. The modeling is done purely in the frequency domain, capturing the typical system level specifications for RF building blocks, independent of the implementation details. A harmonic balance simulation tool has been developed based on those models. The implementation focuses on deterministic effects such as distortion and frequency conversion. The behavioral simulator has been tested for various systems and results are presented.

On the stability of discrete time recursive Volterra filters

Abstract: Many real nonlinear systems are characterized by an infinite input signal memory. In such conditions, system modeling by means of recursive polynomial filters requires a much lower number of coefficients with respect to nonrecursive realizations. However, the main problem of recursive polynomial filters is their inherent instability. This letter describes simple sufficient stability conditions for a class of discrete-time nonlinear systems based on recursive Volterra filters of arbitrary orders.

A partially decoupled RLS algorithm for Volterra filters

Abstract: In this correspondence, we consider a partially decoupled variation of the RLS algorithm. It is based on a constrained optimization of the cumulative filter error using the higher order sets of filter weights to improve on the performance of the lower order weight sets whose values are already established. From this constrained optimization, a recursive algorithm is developed whose form closely resembles the standard Volterra RLS algorithm but with structural differences that arise from eliminating the dependence of the lower order weight sets on the higher order weight sets while retaining the dependence of the higher order weights on the lower order weights. The resulting algorithm, while suboptimal, requires less computational effort than the fully coupled version, converges to steady state in the same amount of time, and is shown by example not to exhibit a substantial degradation in performance.

A non-linear dynamic model for performance analysis of large-signal amplifiers in communication systems

Abstract: A non-linear dynamic model of a large-signal amplifier based on a Volterra-like integral series expansion has been deduced and the measurement procedure for the evaluation of model parameters has been given.

V-vector algebra and its application to Volterra-adaptive filtering

Abstract: In this paper, we describe a new algebraic structure called V-vector algebra, which is a formal basis for the development of Volterra-adaptive filter algorithms as an extension of linear-adaptive techniques. In this way, fast and numerically stable adaptive Volterra filtering algorithms can be easily derived from the known linear theory. V-vector algebra can also be applied to deal with linear multichannel filters with channels of different memory lengths. A reformulation of the Lee-Mathews fast recursive least squares (RLS) algorithm and a new fast and stable Givens rotation-based square root RLS algorithm, both derived using V-vector algebra, are finally presented.

A local form of small gain theorem and analysis of feedback Volterra systems

Abstract: The requirement of evaluating a gain over the entire signal space is one of the restrictions in the traditional small gain theorem. In this paper, a local form of small gain theorem is presented. It yields a bound on the external signal that guarantees that the magnitude of the specified signal along the closed loop stays within a certain region and hence it is useful in addressing the signal magnitude dependent stability problem. The theorem is used to analyze the feedback properties of a Volterra series system as well as an inverse (or pseudo inverse) Volterra system. Improvement over existing results is demonstrated, both theoretically and via numerical examples.

Volterra series analysis and synthesis of a neural network for velocity estimation

Abstract: The motion detection problem occurs frequently in many applications connected with computer vision. Researchers have studied motion detection based on naturally occurring biological circuits for over a century. In this paper, we propose and analyze a motion detection circuit which is based on nerve membrane conduction. It consists of two unidirectional neural networks connected in an opposing fashion. Volterra input-output (I-O) models are then derived for the network so that velocity estimation can be cast as a parameter estimation problem. The technique is demonstrated through simulation.

A reconsideration of the pth-order inverse predistorter

Abstract: The pth-order inverse has been used for nonlinearity compensation for many years. According to pth-order inverse theory, pth-order inverse predistorters and equalizers are identical. However, there is one point often overlooked by many researchers. The pth-order inverse predistorter might change the input signal characteristics so that the Volterra model of the nonlinear system to be compensated, and upon which the pth-order inverse predistorter is designed, can no longer capture the nonlinear system behavior. This phenomenon will degrade the performance of the pth-order inverse predistorter. This performance degradation of a pth-order inverse predistorter becomes more serious when the Volterra model of the nonlinear system is derived for simple testing signals such as PSK. This important, yet often overlooked, phenomenon is investigated in detail.

A Volterra mapping-based S-parameter behavioral model for nonlinear RF and microwave circuits and systems

Abstract: This paper presents a Volterra mapping-based S-parameter equivalent model for nonlinear RF/microwave circuits and systems. In this S-parameter-oriented approach to behavioral modelling, the linear part and the nonlinear parts are independent and have their own physical definitions. It is straightforward to obtain estimates of linear and nonlinear distortion by using the model parameters, as well as obtaining predictions of the behaviour of nonlinear networks.

Multichannel linear and quadratic adaptive filtering based on the Chandrasekhar fast algorithm

Abstract: A new fast algorithm for multichannel linear and quadratic adaptive filtering using the Chandrasekhar equations is presented. Based on the shift-invariance property, the multichannel linear model could be described by a time-invariant state-space model to which we apply the Chandrasekhar factorization technique, which provides interesting numerical properties. Furthermore, a new method for nonlinear filtering is given where the multichannel Chandrasekhar algorithm is applied on the second-order Volterra (SOV) filter after suitable transformations.

Nonlinear distortion model for VCO-PLL FM transmission systems

Abstract: The nonlinear distortion of frequency or phase modulation systems composed by a voltage-controlled oscillator (VCO) modulator and a phase-locked loop (PLL) discriminator is addressed. Volterra series nonlinear transfer functions up to third order, for an LC Colpitts type modulator and a PLL with simultaneous nonlinear phase-detector and VCO, are combined as a cascade of mildly nonlinear systems. This approach gives a fully analytical description of that complex arrangement, which allowed the derivation of theoretical linearization conditions for that FM/PM modem.

Volterra model for the imaging mechanism of ocean surface currents by synthetic aperture radar

Abstract: The imaging mechanism of ocean surface current gradients by synthetic aperture radar (SAR) is nonlinear. The authors propose a Volterra series expansion as a tool for obtaining an input-output relationship between the current and the SAR image pixel. With this model one can study the behavior of each nonlinear component as a function of several parameters (current magnitude and direction, wind speed, equilibrium spectrum parameterization, etc.).

New techniques for vibration condition monitoring : Volterra kernel and Kolmogorov-Smirnov

Abstract: This research present a complete review of signal processing techniques used, today, in vibration based industrial condition monitoring and diagnostics. It also introduces two novel techniques to this field, namely: the Kolmogorov-Smimov test and Volterra series, which have not yet been applied to vibration based condition monitoring. The first technique, the Kolmogorov-Smimov test, relies on a statistical comparison of the cumulative probability distribution functions (CDF) from two time series. It must be emphasised that this is not a moment technique, and it uses the whole CDF, in the comparison process. The second tool suggested in this research is the Volterra series. This is a non-linear signal processing technique, which can be used to model a time series. The parameters of this model are used for condition monitoring applications. Finally, this work also presents a comprehensive comparative study between these new methods and the existing techniques. This study is based on results from numerical and experimental applications of each technique here discussed. The concluding remarks include suggestions on how the novel techniques proposed here can be improved.

Input-Output Analysis

Abstract: In this chapter we introduce the reader to various methods for the input-output analysis of nonlinear systems. The methods are divided into three categories: 1. Optimal Linear Approximants for Nonlinear Systems. This is a formalization of a technique called the describing function technique, which is popular for a quick analysis of the possibility of oscillation in a feedback loop with some nonlinearities in the loop. 2. Input-output Stability. This is an extrinsic view to the stability of nonlinear systems answering the question of when a bounded input produces a bounded output. This is to be compared with the intrinsic or state space or Lyapunov approach to stability in the next two chapters. 3. Volterra Expansions for Nonlinear Systems. This is an attempt to derive a rigorous “frequency domain” representation of the input output behavior of certain classes of nonlinear systems.

Reduced order modeling for low Reynolds number flow control

Abstract: This paper presents recent analytical and experimental research to modify and control low Reynolds number flows over prototypical airfoils associated with micro-air-vehicles The simplified experimental test geometry consists of a meso-scale piezoceramic actuated flap that undergoes peak amplitude displacements of 40 microns The flap actuator array is designed to modify separation and reattachment location on the airfoil The location of the reattachment on the upper surface of the prototypical airfoil is measured by an array of MEM's shear stress sensors located downstream The focus of this paper is the discussion of the status and applicability of reduced order modeling techniques for the derivation of active feedback flow control strategies for the prototypical active airfoil Frequently, reduced order models are derived from a library of component fluid modes which serve as the basis for a low dimensional approximation of the nonlinear Navier Stokes equations The methodology discussed in this paper differs markedly from these approaches We derive a technique employing multiresolution and wavelet approximations of nonlinear Volterra series that represent the input-output dynamics of the system The accuracy of the resultant low- dimensional input-output models is validated on a benchmark nonlinear aeroelastic testbed

Analyses of distortions and cross modulations in erbium-doped fiber amplifiers

Abstract: The closed-form expressions of nonlinear Fourier transfer functions are presented for the analyzes of distortions and cross modulations in erbium-doped fiber amplifier (EDFA) systems. Based upon Volterra series and the time-dependent perturbation theory, the transfer functions are obtained after taking account of both the EDFA nonlinearity and chirping effect. Their applications to an AM-SCM and an eight-channel wavelength-division-multiplexed systems are demonstrated.

Nonlinear cross talk cancellation for high density optical recording

Abstract: This paper deals with cross talk cancellation for high density optical recording. The data density can be increased reducing the track pitch, as long as cross talk is kept under control. To cope with interference from adjacent tracks, we propose and analyze an adaptive nonlinear cross talk canceller based on a three spot detection system. The optical channel is accurately modeled by a two-dimensional Volterra series. For the sake of simplicity, the performance comparisons presented in this paper are based on the assumption that noise is additive, white, and Gaussian (AWGN model). Simulation results show the effectiveness of the proposed cross talk canceller.

Frequency based nonlinear controller design of regulating systems subjected to time domain constraints

Abstract: Presented is a nonlinear controller design methodology for a class of regulating systems subjected to quantitative time domain constraints. The output and actuator saturation performance specifications are given as allowable time domain tolerances. The controller design is executed in the frequency domain and is applicable when the frequency response of a linear design cannot satisfy the gain and phase characteristics required by quantitative time domain specifications. A describing function (DF) approach, automated by the Volterra series, facilitates the nonlinear controller design. The resulting gain and phase distortions associated with the DF of the dynamic nonlinear element are used to achieve the desirable open loop gain and phase characteristics identified by the time domain constraints. The design methodology is illustrated on the idle speed control of a Ford 4.6L V-8 fuel injected engine. The engine input is the by-pass air valve and the regulated output is engine speed. The power steering pump generates the nonmeasureable external torque load.

Dynamic Measurements of Low-Frequency Loudspeakers Modeled by Volterra Series

Abstract: This paper describes the application of a general mathematical method to the identification of low-frequency loudspeaker systems Third-order Volterra series are applied to match the measured harmonic distortion responses of three commercial low-frequency loudspeaker systems with simulation results This allows to compute the non-linear parameters of the loudspeaker, used within standard physical models The proposed approach can be used as a general method to define loudspeaker dynamic models, exploiting standard acoustic pressure measurements, instead of displacement variation [ 11 1 Loudspeaker modeling Until now loudspeakers have been modeled, following the well-known Small-Thiele approach [2], that describes their behavior at low frequencies and small input power, and produces a linear transfer function Unfortunately it does not match our requirements; first of all because it is a liner model and moreover as it does not describe accurately real Sound Pressure Level (SPL) curves In the following the Small-Thiele model will be considered, extending it by introducing the displacement dependence in the electrical and mechanical parameters This allows to obtain an effective relationship between the electrical input and the acoustic output Therefore we assume that the following equations hold e(t) &i(t) L(x)? = Bl(z)i(t) U(i) = Sri(i) F(i) R&i(t) A&&i K(+-c = p(t)S, p(t) = SJ$ + sJ3g *This work was supported by ASK Industries and by EC under ESPRIT ESD project 28583 (1)

Zero forcing equalization of multiuser time-varying nonlinear systems

Abstract: Multiuser communication systems which experience intersymbol interference and nonlinearities can be modeled using the Volterra series. In this paper we consider the design of a linear multichannel zero forcing equalizer for a multiuser Volterra (nonlinear) system. Time-variations in the Volterra systems are modeled using basis expansions, and equivalent multiple-input time-invariant systems are derived. Equalizers are designed from the channel matrix and a training sequence, and complex exponential basis frequencies are estimated. Simulations demonstrate the effectiveness of the equalizer on a number of different systems.

Tracking control of a pendulum using a numerically efficient state estimation approach for polynomic non-linear systems

Abstract: This paper reports on the tracking control of a pendulum. The particular contributions of this paper lie in the development of a numerically efficient approach for the state estimation of a class of non-linear systems which fall under the extended generalized Wiener model structure and its application to the pendulum system. It details the estimation and control aspects for achieving the tracking control of the pendulum where attention is focused on Extended Kalman Filtering (EKF) methods based on Volterra series approximations of the non-linearity for the estimation of the pendulum states. Control is then effected by the Feedback Linearization (FL) technique and the Internal Model Principle (IMP). It is argued that this offers accuracy benefits over linear techniques while substantially reducing the computational burden associated with the standard EKF approaches. The arguments are supported by evidence from a case study system. It is demonstrated that this proposed approach is significantly faster and d...

Identification of nonlinear communication channel using evolutionary Volterra time-series

Abstract: Building a suitable model for a nonlinear channel is a major problem for communication systems. Finding a suitable model for the channel depends mainly on the type of nonlinearity of the channel and the approach to which the model parameters are estimated. Traditional approaches for parameter identification have difficulty in estimating nonlinear system parameters with a limited number of measurements. We explore the use of evolutionary strategies (ESs) as the key search approach of a methodology for estimating the parameters of the discrete Volterra time series to model nonlinear communication channels. An example is presented to illustrate the effectiveness of the proposed approach as compared to the least squares approach.