Showing papers on "Volterra series published in 1982"
TL;DR: Using a novel approach, the amplitude and frequency of nearly sinusoidal nonlinear oscillators can be calculated by solving two algebraic nonlinear equations using a recursive algorithm based on Volterra series.
Abstract: Using a novel approach, the amplitude and frequency of nearly sinusoidal nonlinear oscillators can be calculated by solving two algebraic nonlinear equations. These determining equations can be generated to within any desired accuracy using a recursive algorithm based on Volterra series. Our method inherits many desirable features of the harmonic balance method, the describing function method, and the averaging method. Our technique is analogous to, but is much simpler than, the classic approach due to Krylov, Bogoliubov, and Mitropolsky. Unlike conventional techniques, however, our approach imposes no severe restriction on either the degree of nonlinearity, or the amplitude of oscillation. Moreover, the accuracy of the solution can be determined by a constructive algorithm.
84 citations
01 May 1982
TL;DR: This paper deals with a class of nonlinear, time-invariant systems with memory based on the truncation of discrete-time Volterra series expansions of input-output relationships, which can be implemented by a finite-length transversal filter, a finite number of multipliers, and a summing bus.
Abstract: This paper deals with a class of nonlinear, time-invariant systems with memory - called discrete Volterra processors - based on the truncation of discrete-time Volterra series expansions of input-output relationships. These systems can be implemented by a finite-length transversal filter, a finite number of multipliers, and a summing bus, and share the interesting property of being described by a linear combination of suitable nonlinear functions of the input samples. Two examples of application are considered in some detail: (i) The design of minimum mean-square error predictors of discrete-time random processes, and (ii) The identification of discrete nonlinear systems with memory.
36 citations
TL;DR: In this article, it was shown that continuous-time regular (or bilinear) systems or discrete-time stateaffine systems have a similar property to the Volterra series.
29 citations
TL;DR: In this article, a new operational calculus for computing the response of nonlinear systems to various deterministic excitations is presented, which is a natural generalization of the nonlinear domain of the Heaviside operational calculus.
21 citations
TL;DR: A functional approach has been developed to represent continuous separable, nonlinear systems of a general type based on a modified Volterra series that has particular significance in the development of identification procedures based on cross-correlation functions, as these functions can now be estimated practically without any influence from the bias level.
11 citations
14 Jun 1982
TL;DR: In this paper, a functional expansion of the output of a nonlinear discrete-time system described by analytic functions is proposed in terms of tensor products of differential operators, where the control acts linearly or in case of systems given by polynomial difference equations.
Abstract: Given a nonlinear discrete-time system described by analytic functions, a functional expansion of the output is proposed In the general case a formula is derived in terms of tensor products of differential operators When the controls act linearly or in case of systems given by polynomial difference equations, this development yields a discrete-time Volterra series In that case, the Volterra kernels can be explicitly exhibited by means of straightforward algebraic computations
10 citations
05 Apr 1982
TL;DR: A MACSYMA implementation of a method to obtain decoupling of nonlinear systems by means of state-feedback is presented and the cases of rejection of disturbances and noninteracting control are treated.
Abstract: A MACSYMA implementation of a method to obtain decoupling of nonlinear systems by means of state-feedback is presented. The cases of rejection of disturbances and noninteracting control are treated.
8 citations
TL;DR: In this paper, a linearization approach to self-tuning control of a nonlinear process is considered, where the process input nonlinearity is assumed to be separable from the linear part.
4 citations
TL;DR: In this paper, the response of a bilinear dynamical system in terms of a Volterra series is characterized in the frequency domain, and the zero harmonic component of the output of a closed-loop system comprised of the bilinearly system and a static relay nonlinear element is approximated using basic second-order VOLTERRA kernels.
Abstract: After expressing the response of a bilinear dynamical system in terms of a Volterra series, the filtering properties of the system are characterized in the frequency domain. The zero harmonic component of the output of a closed-loop system comprised of the bilinear system and a static relay non-linear element is approximated using basic second-order Volterra kernels. This allows estimation of bilinear system parameters based upon measurements of the average value of the closed-loop system output.
4 citations
TL;DR: In this paper, a state-affine realization theory for a Volterra series input-output map is presented, which involves the definition of certain shift operators on linear spaces associated with the transforms of the kernels in the VOLTERRA series.
Abstract: Using a transform representation, a state-affine realization theory for a Volterra series input-output map is presented. The approach involves the definition of certain shift operators on linear spaces associated with the transforms of the kernels in the Volterra series. The result is a realization algorithm that is extremely easy to implement. The approach also yields a theory of minimality, span-reachability, and observability for infinite degree state-affine systems.
3 citations
TL;DR: In this article, a separability property of the Volterra kernels is shown to be necessary and sufficient for local realizability, which is not the case for the Lipschitz kernels.
TL;DR: In this paper, the computation of nonlinear polarization terms and/or susceptivity tensors in media at optical frequencies is outlined in the framework of the Volterra-series method, which allows us to take into account the difference between local and macroscopic field in a general, simple and systematic way.
Abstract: The computation of nonlinear polarization terms and/or susceptivity tensors in media at optical frequencies is outlined in the framework of the Volterra-series method. The referred approach is fully consistent with the usual form of nonlinear constitutive relationships and allows us to take into account the difference between local and macroscopic field in a general, simple and systematic way.
TL;DR: In this paper, a new technique based on the Volterra characterisation of nonlinear systems is presented for the identification of systems in which the nonlinear element is in the feedback path.
TL;DR: A functionnal approach is developed to represent continuous nonlinear imaging systems based on VOLTERRA series that leads to a discrete model appropriate for digital storage or images processing.
01 May 1982
TL;DR: By using a new and efficient nonlinear frequency domain adaptive algorithm, a nonlinear model for a hybrid in an actual connection has been identified and is found to be 8 db more accurate than the linear model.
Abstract: In most applications of adaptive filtering algorithms to the telephone echo cancellation problem, a linear model is assumed for the hybrid. In this paper, a nonlinear model based on a Volterra series representation is adopted. By using a new and efficient nonlinear frequency domain adaptive algorithm, a nonlinear model for a hybrid in an actual connection has been identified. The nonlinear model is found to be 8 db more accurate than the linear model. The problem of automatic gain control in the design of a full-duplex telephone network with LPC vocoder in the loop, and its interaction with the echo canceller and the hybrid nonlinearity is also discussed.