Showing papers on "Volterra series published in 2001"

Adaptive Volterra filters for active control of nonlinear noise processes

Abstract: This paper presents a Volterra filtered-X least mean square (LMS) algorithm for feedforward active noise control. The research has demonstrated that linear active noise control (ANC) systems can be successfully applied to reduce the broadband noise and narrowband noise, specifically, such linear ANC systems are very efficient in reduction of low-frequency noise. However, in some situations, the noise that comes from a dynamic system may he a nonlinear and deterministic noise process rather than a stochastic, white, or tonal noise process, and the primary noise at the canceling point may exhibit nonlinear distortion. Furthermore, the secondary path estimate in the ANC system, which denotes the transfer function between the secondary source (secondary speaker) and the error microphone, may have nonminimum phase, and hence, the causality constraint is violated. If such situations exist, the linear ANC system will suffer performance degradation. An implementation of a Volterra filtered-X LMS (VFXLMS) algorithm based on a multichannel structure is described for feedforward active noise control. Numerical simulation results show that the developed algorithm achieves performance improvement over the standard filtered-X LMS algorithm for the following two situations: (1) the reference noise is a nonlinear noise process, and at the same time, the secondary path estimate is of nonminimum phase; (2) the primary path exhibits the nonlinear behavior. In addition, the developed VFXLMS algorithm can also be employed as an alternative in the case where the standard filtered-X LMS algorithm does not perform well.

Identification and Control Using Volterra Models

Abstract: 1. Introduction.- 2. Qualitative Behavior.- 3. Restrietions & Extensions.- 4. Determination of Volterra Model Parameters.- 5. Practical Considerations in Volterra Model Identification.- 6. Model-Based Controller Synthesis.- 7. Advanced Direct Synthesis Controller Design.- 8. Model Predictive Control Using Volterra Series.- 9. Application Case Studies.- 10. Summary.

Optimal Volterra kernel estimation algorithms for a nonlinear communication system for PSK and QAM inputs

Abstract: A fifth-order Volterra kernel estimation algorithm, which is optimal in the least mean square error sense, for a bandpass nonlinear system is derived. The algorithm is based on some characteristics of i.i.d. circularly symmetric zero-mean complex-valued Gaussian random variables. The proposed algorithm can be used to identify a nonlinear system under uniformly i.i.d. rectangular M-QAM input and under uniformly i.i.d. M-PSK input (M/spl ges/4) with modest modification. The same approach has been used to derive an optimal Volterra kernel estimation algorithm up to the third order. However, in some cases, a third-order model is not of "high enough order" to capture the nonlinear system characteristics. A simulation example is given to show the necessity of deriving a fifth-order Volterra kernel estimation algorithm and to test for the correctness of the algorithm.

Reduced complexity Volterra models for nonlinear system identification

Abstract: A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter’s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a fixed pole expansion technique (FPET) within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex) pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed.

Efficient temporal processing with biologically realistic dynamic synapses.

Abstract: Synapses play a central role in neural computation: the strengths of synaptic connections determine the function of a neural circuit. In conventional models of computation, synaptic strength is assumed to be a static quantity that changes only on the slow timescale of learning. In biological systems, however, synaptic strength undergoes dynamic modulation on rapid timescales through mechanisms such as short term facilitation and depression. Here we describe a general model of computation that exploits dynamic synapses, and use a backpropagation-like algorithm to adjust the synaptic parameters. We show that such gradient descent suffices to approximate a given quadratic filter by a rather small neural system with dynamic synapses. We also compare our network model to artificial neural networks designed for time series processing. Our numerical results are complemented by theoretical analyses which show that even with just a single hidden layer such networks can approximate a surprisingly large class of nonlinear filters: all filters that can be characterized by Volterra series. This result is robust with regard to various changes in the model for synaptic dynamics.

On the reliability of the surrogate data test for nonlinearity in the analysis of noisy time series

Abstract: In the analysis of real world data, the surrogate data test is often performed in order to investigate nonlinearity in the data. The null hypothesis of the test is that the original time series is generated from a linear stochastic process possibly undergoing a nonlinear static transform. We argue against reported rejection of the null hypothesis and claims of evidence of nonlinearity based on a single nonlinear statistic. In particular, two schemes for the generation of surrogate data are examined, the amplitude adjusted Fourier transform (AAFT) and the iterated AAFT (IAFFT) and many nonlinear discriminating statistics are used for testing, i.e. the fit with the Volterra series of polynomials and the fit with local average mappings, the mutual information, the correlation dimension, the false nearest neighbors, the largest Lyapunov exponent and simple nonlinear averages (the three point autocorrelation and the time reversal asymmetry). The results on simulated data and real data (EEG and exchange rates) suggest that the test depends on the method and its parameters, the algorithm generating the surrogate data and the observational data of the examined process.

Distortion analysis of periodically switched nonlinear circuits using time-varying Volterra series

Abstract: This paper presents a new frequency-domain method for distortion analysis of general periodically switched nonlinear circuits. It generalizes Zadeh's time-varying network functions and bifrequency transfer functions from linear time-varying systems to nonlinear time-varying systems. The periodicity of time-varying network functions of linear and nonlinear periodically time-varying systems is investigated using time-varying Volterra series. We show that a periodically switched nonlinear circuit can be characterized by a set of coupled periodically switched linear circuits. Distortion of the periodically switched nonlinear circuit is obtained by solving these linear circuits. This result is a generalization of the multi-linear theory known for nonlinear time-invariant circuits. We also show that the aliasing effect encountered in noise analysis of switched analog circuits exists in distortion analysis of periodically switched nonlinear circuits. Computation associated with the folding effect can be minimized by using the adjoint network of periodically switched linear circuits, in particular, the frequency reversal theorem. The method presented in this paper has been implemented in a computer program. Distortion of practical switched circuits is analyzed and the results are compared with SPICE simulation.

Highly linear CMOS RF MMIC amplifier using multiple gated transistors and its Volterra series analysis

Abstract: CMOS RF MMIC amplifiers are fabricated with linearization technique using multiple gated transistors. At 900 MHz, double and triple gated amplifiers show 2.5-4.5 dB larger figure of merit (linearity-DC power consumption), which means that only 1/2/spl sim/1/3 of DC power is needed to obtain the same OIP/sub 3/ value. Using Volterra series analysis and harmonic balance simulation, it is shown that the linearization technique with the 2nd harmonic termination can increase IIP/sub 3/ by amount of 16 dB max. without additional DC power consumption at optimal bias condition, which can reduce more than 90% of DC power consumption with the same linearity performance.

A simplified predistorter for compensation of nonlinear distortion in OFDM systems

Abstract: This paper presents a new simplified predistortion scheme to compensate nonlinear distortion introduced by the high power amplifier (HPA) in OFDM systems. OFDM systems are susceptible to HPA nonlinearities in particular because of their large peak-to-average power ratios. Previously, a Volterra-based predistorter was suggested for compensation of HPA's nonlinear distortion in OFDM systems. In contrast to this earlier work, our adaptive predistorter utilizes a more simplified structure. It is shown that the new simplified structure exhibits faster convergence than the previous Volterra-based predistorter. In addition, the performance of the new predistortion scheme for OFDM systems is evaluated in terms of total degradation, optimal output backoff, and BER. Simulation results also show that our predistortion scheme is more efficient in compensating the nonlinear distortion of HPAs in OFDM systems than the previous scheme.

Reduced-Order Modeling: Cooperative Research and Development at the NASA Langley Research Center

Abstract: Cooperative research and development activities at the NASA Langley Research Center (LaRC) involving reduced-order modeling (ROM) techniques are presented. Emphasis is given to reduced-order methods and analyses based on Volterra series representations, although some recent results using Proper Orthogonal Decomposition (POD) are discussed as well. Results are reported for a variety of computational and experimental nonlinear systems to provide clear examples of the use of reduced-order models, particularly within the field of computational aeroelasticity. The need for and the relative performance (speed, accuracy and robustness) of reduced-order modeling strategies is documented. The development of unsteady aerodynamic state-space models directly from CFD analyses is presented in addition to analytical and experimental identifications of Volterra kernels. Finally, future directions for this research activity are summarized.

Volterra series approach for nonlinear aeroelastic response of 2-d lifting surfaces

Abstract: The problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via Volterra series approach is addressed. The related aeroelastic governing equations are based upon the inclusion of structural nonlinearities, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of geometric nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

Multiresolution Methods for Reduced-Order Models for Dynamical Systems

Abstract: Reduced-orderinput/output models arederived for a class of nonlinearsystems by utilizing wavelet approximationsof kernels appearing in Volterra series representations. Although Volterra series representationsof nonlinear system input/output have been understood from a theoretical standpoint for some time, their practical use has been limited as a result of the dimensionality of approximations of the higher-order, nonlinear terms. In general, wavelets and multiresolution analysis have shown considerable promise for the compression of signals, images, and, most importantly here, some integral operators. Unfortunately, causal Volterra series representations are expressed in terms of integrals that are restricted to products of half-spaces, and there is a signie cant dife culty in deriving wavelets that are appropriate for Volterra kernel representations that are restricted to semi-ine nite domains. In addition, it is necessary to derive Volterra kernel expansions that are consistent with the method of sampling used to obtain the input and output data. This paper derives discrete approximations for truncated Volterra series representations in termsof a specie cclass of biorthogonal wavelets. When a zero-orderhold is used for both the input and output signals, it is shown that a consistent approximation of the input/output system is achieved for a specie c choice of biorthogonal wavelet families. This family is characterized by the fact that all of the wavelets are biorthogonal with respect to the characteristic function of the dyadic intervals used to dee ne the zero-order hold. It is also simple to show that an arbitrary choice of wavelet systems will not, in general, provide a consistent approximation for arbitrary input/output mappings. Numerical studies of the derived methodologies are carried out by using experimental pitch/plunge response data from the TAMU Nonlinear Aeroelastic Testbed.

Intermodulation nulling in HEMT common source amplifiers

Abstract: A new model of the second- and third-order intermodulation products from HEMT and MESFET small-signal amplifiers, resulting from nonlinear drain-source current has been proposed in our previous publications. Based on this model, intermodulation nulling conditions in terms of the Taylor series coefficients, hence in terms of bias, have been investigated. This paper now examines the load dependence of the second- and third-order intermodulation products in HEMT small-signal common source amplifiers. Intermodulation nulling conditions are proposed and validated. This is useful in designing a high performance amplifier by calculation of optimum load for minimum distortion and studying distortion generation as a function of circuit topology.

Identification of input-output bilinear systems using cumulants

Abstract: This paper is concerned with the identification of a discrete input-output bilinear system driven by an independent identically distributed (i.i.d.) stochastic input and corrupted by measurement noise. A novel algorithmic procedure for the direct computation of the unknown model parameters is developed based on crosscumulant information up to third order. Simulations and comparisons with a least squares type identification method are provided.

Second-order adaptive Volterra system identification based on discrete nonlinear Wiener model

Abstract: The authors present the nonlinear LMS adaptive filtering algorithm based on the discrete nonlinear Wiener model for second-order Volterra system identification application. The main approach is to perform a complete orthogonalisation procedure on the truncated Volterra series. This allows the use of the LMS adaptive linear filtering algorithm for calculating all the coefficients with efficiency. This orthogonalisation method is based on the nonlinear discrete Wiener model. It contains three sections: a single-input multi-output linear with memory section, a multi-input, multi-output nonlinear no-memory section and a multi-input, single-output amplification and summary section. For a white Gaussian noise input signal, the autocorrelation matrix of the adaptive filter input vector can be diagonalised unlike when using the Volterra model. This dramatically reduces the eigenvalue spread and results in more rapid convergence. Also, the discrete nonlinear Wiener model adaptive system allows us to represent a complicated Volterra system with only few coefficient terms. In general, it can also identify the nonlinear system without over-parameterisation. A theoretical performance analysis of steady-state behaviour is presented. Computer simulations are also included to verify the theory.

Optimal control of a continuous bioreactor using an empirical nonlinear model

Abstract: Nonlinear model-based controllers are developed to regulate the cell biomass exit concentration of a continuous-flow bioreactor by manipulating the dilution rate. Plant-friendly input sequences are used to identify a second-order Volterra series model from a virtual plant. A Volterra-Laguerre model is produced by projection onto the orthonormal Laguerre basis functions. A partitioned nonlinear inverse (PNLI) controller is synthesized and is shown to be nominally stable over the manipulated variable range [0.941, 0.999]h -1 using the structured singular value. A referenced-based switching algorithm is incorporated to improve the robustness and stability characteristics of the closed-loop system. Nonlinear model predictive control (NMPC) alleviates the need for the switching controller, and an analytical NMPC solution incorporating recursive least squares avoids entrapment in local objective function minima. This controller offers optimum tracking for unreachable setpoints as well as tracking of the constrained local minimum for input-magnitude-constrained problems modeled by second-order Volterra-Laguerre systems.

Measurement-based nonlinear modeling of spectral regrowth

Abstract: This paper investigates the ability of nonlinear models extracted from measured continuous wave amplifier data to predict the amplifier response to modulated signals in compression. Experimental verification of the nonlinear model prediction is performed using nonlinear vectorial network analyzer measurements.

Predicting Hyper-Chaotic Time Series Using Adaptive Higher-Order Nonlinear Filter

Abstract: A newly proposed method, i.e. the adaptive higher-order nonlinear finite impulse response (HONFIR) filter based on higher-order sparse Volterra series expansions, is introduced to predict hyper-chaotic time series. The effectiveness of using the adaptive HONFIR filter for making one-step and multi-step predictions is tested based on very few data points by computer-generated hyper-chaotic time series including the Mackey-Glass equation and four-dimensional nonlinear dynamical system. A comparison is made with some neural networks for predicting the Mackey-Glass hyper-chaotic time series. Numerical simulation results show that the adaptive HONFIR filter proposed here is a very powerful tool for making prediction of hyper-chaotic time series.

On the convergence of Volterra filter equalizers using a pth-order inverse approach

Abstract: The pth-order inverse method is one of important approaches to Volterra equalization. However, when a pth-order Volterra equalizer instead of an exact Volterra equalizer is connected in cascade before (after) a nonlinear system, the existence of Volterra filter equalization and the approximation output error bound of the resulting system have yet to be reported. In this paper, the concept of local l/sup 2/ stability for a Volterra system is introduced, and the algorithmic formulae of a pth-order inverse equalizer via a multidimension z-transform are presented. The output error signal and the approximation output error bound of the resulting system are investigated as well. It is shown that the approximation output error tends to zero as p tends to infinity for a finite range of input amplitude values. Finally some simulation results are presented and discussed.

Time-varying Volterra-series analysis of spectral regrowth and noise power ratio in FET mixers

Abstract: This paper presents a direct and robust analysis technique for evaluating nonlinear distortion phenomena in FET mixers excited by multitone signals. Time-varying Volterra-series analysis has previously been proven to be appropriate for small-signal intermodulation-distortion calculations in mixers excited by simple RF signals. Spectral convolutions of the suitably mapped control voltages are introduced in this paper in order to solve the nonlinear current source calculations for narrow-band modulated or broad-band multicarrier RF signals. Simulations and measurements of a properly characterized resistive mixer validate the accuracy of this direct and noniterative analysis tool for spectral regrowth and noise-power-ratio prediction in such applications.

Z+ fading memory and extensions of input–output maps

Abstract: An Erratum for this article has been published in the International Journal of Circuit Theory and Applications 30(4) 2002, 179. Much is known about time-invariant non-linear systems with inputs and outputs defined on Z+ that possess approximately-finite memory. For example, under mild additional conditions, they can be approximated arbitrarily well by the maps of certain interesting simple structures. An important fact that gives meaning to results concerning such systems is that the approximately-finite-memory condition is known to be often met. Here we consider the known proposition that if a causal time-invariant discrete-time input–output map H has fading memory on a set of bounded functions defined on all of the integers Z, then H can be approximated arbitrarily well by a finite Volterra series operator. We show that in a certain sense, involving the existence of extensions of system maps, this result too has wide applicability. Copyright © 2001 John Wiley & Sons, Ltd.

Identification of Volterra kernels using interpolation

Abstract: The paper presents a new method for the identification of frequency-domain Volterra kernels. Based on the assumption that frequency-domain kernels are focally smooth, the kernel surface can be approximated by interpolation techniques, thus reducing the complexity of the model. Similarly to the unreduced (Volterra) model, this smaller model is also (i) linear in the unknowns, (ii) only locally sensitive to its parameters and (iii) free of structural assumptions about the system. The parameter estimation boils down to solving a linear system of equations in the least-squares (LS) sense. The design of the interpolation scheme is described, and the performance of the approximation is analyzed, and illustrated by simulation. The algorithm allows a significant saving in measurement time compared to other kernel estimation methods.

Nonlinear Stability and Response of Lifting Surfaces Via Volterra Series

Abstract: This investigation concerns the time and frequency formulations of non-linear two-dimensional lifting surfaces exposed to an incompressible flow field and subjected to an external pressure pulse. In order to address this problem, Volterra series approach in conjunction with the multidimensional Laplace transform is used. This methodology enabling one to solve the aeroelastic governing equations of lifting surfaces opens the way to connect this methodology with that based on neural networks and NARMAX/NARX networks models. Moreover, this extended way to address this problem constitutes a good basis for treatment of the theory of 3D lifting surfaces.

A pipeline architecture of quadratic adaptive Volterra filters based on NLMS algorithm

Abstract: This paper proposes a pipeline implementation of quadratic adaptive Volterra filters based on NLMS algorithm for high-speed processing and low power consumption. This implementation also gives a superior convergence performance than that of LMS pipeline algorithm under the colored inputs condition. The proposed implementation has zero output latency and reduced critical path compared to the non-pipelined implementation.

A new feedforward neural network hidden layer neuron pruning algorithm

Abstract: This paper deals with a new approach to detect the structure (i.e. determination of the number of hidden units) of a feedforward neural network (FNN). This approach is based on the principle that any FNN could be represented by a Volterra series such as a nonlinear input-output model. The new proposed algorithm is based on the following three steps: first, we develop the nonlinear activation function of the hidden layer's neurons in a Taylor expansion, secondly we express the neural network output as a NARX (nonlinear autoregressive with exogenous input) model and finally, by appropriately using the nonlinear order selection algorithm proposed by Kortmann-Unbehauen (1988), we select the most relevant signals on the NARX model obtained. Starting from the output layer, this pruning procedure is performed on each node in each layer. Using this new algorithm with the standard backpropagation (SBP) and over various initial conditions, we perform Monte Carlo experiments leading to a drastic reduction in the nonsignificant network hidden layer neurons.

Distortion analysis of high-frequency log-domain filters using Volterra series

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.