Showing papers on "Volterra series published in 1981"

On the Theory of Bilinear Time Series Models

Abstract: SUMMARY The theory of bilinear time series models is considered in this paper The sufficient conditions for asymptotic stationarity of the bilinear time series models are derived, and the expressions for the variance and covariance are obtained The conditions for the invertibility of the model are also included The estimation of the parameters of the scalar bilinear time series model is considered The bilinear models are fitted to sunspot numbers and also to a P-wave of a nuclear explosion The forecasting of sunspot numbers is also considered

Dynamical Realizations of Finite Volterra Series

Abstract: In this paper, realizations of finite Volterra series are viewed as nonlinear analytic input–output systems, with state space described by an analytic manifold. For a minimal realization guaranteed by H. J. Sussmann, the state space, which is unique up to diffeomorphism, is shown to have the homogeneous space structure of a nilmanifold, the quotient of two nilpotent Lie groups. The structure of nilmanifolds as described by A. Malcev is used to show that for these systems, the state space has a vector space structure. As a consequence of this result, it is shown that a minimal realization of a finite Volterra series can be described as a cascade of linear subsystems with polynomial link maps, in which the dimension o f each linear subsystem is independent of the realization considered.

Frequency domain non-linear adaptive filter

Abstract: A new non-linear adaptive filter is presented. The algorithm is based on the Volterra series implemented in the frequency domain. For a finite memory of length N, the algorithm converges to the equivalent time domain non-linear adaptive filter as proposed by Roy and Sherman [1]. The frequency domain implementation offers a significant reduction in computation. For the second order Volterra series, the proposed algorithm requires O(N2) multiply-adds for N output points as opposed to an O(N3) for the time domain algorithm. For a large number of taps (≥ 32), the linear version of the proposed algorithm also offers a significant reduction in computation. Another advantage is its fast convergence to the Wiener solution due to the "pseudo-orthogonality" obtained by adapting in the frequency domain.

Volterra series representation of a forward-biased p-i-n diode

Abstract: A nonlinear model is proposed for a forward-biased p-in diode controlled by an ac signal consisting of a group of sinusoidal signals. The model is applicable to these phases of diode operation where linearized basic physical equations are valid. Current-voltage relations have been obtained for junctions and the "i" region in the form of a Taylor series with frequency-dependent coefficients. The new model is valid for signal levels considerably exceeding those admissible for the known linear model [3], [4]. A new form of signal limiting condition, suitable for measurement verification and calculations, has been obtained. The Volterra series for the equations representing the diode has been found which correspond to the Taylor series obtained. The convergency condition for this series is identical to that for thel Taylor series. The conformability of measurement and calculation results fully testifies to the usefulness of the proposed model for nonlinear distortion analysis.

Minimal-order realizations for continuous-time two-power input-output maps

Abstract: This paper considers two-power input-output maps which are continuous-time, impulsive, and time-invariant. Realizability, by a very general class of nonlinear differential systems, is characterized simply in terms of the symmetric Volterra transfer function. The characterization leads directly to a family of minimal-order realizations having the (feedforward) structure described by Crouch [6]. Members of the family have states which are related by quadratic homeomorphisms. An especially simple member of the family serves as a canonical form. The development is self-contained and unlike Crouch's requires only elementary mathematical tools.

Volterra series analysis of MESFET mixers

Abstract: Conversion gain in a MESFET gate mixer is analysed using a Volterra series representation. The transistor model includes the input gate capacitance non-linearity and the output, bi-dimensional non-linearity. Guidelines for optimum primary terminations on the RF and IF sides of the transistor are obtained, and analysis results are compared to an experimental mixer with 12 dB conversion gain.

Abstract bilinear systems: The forward shift approach

Abstract: A bilinear realization theory for a Volterra series input-output map is given. The approach involves a special transform representation for a Volterra series and certain shift operators on a Fock space. The approach yields in a very simple manner a theory of span reachability, observability and minimality for bilinear systems.