Volterra series

About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.

Optimal Nonlinear Filtering

Abstract: Publisher Summary This chapter focuses on optimal nonlinear filtering. An approach to nonlinear filtering problems uses functional Volterra series expansions. This approach requires the solution of integral equations and is not easily applied unless the system input-output characteristics are given in the form of functionals rather than as differential equations. The solution is then in the form of functionals, and no easy and direct method exists for actually synthesizing the filter from the functional solution. This method also appears to be limited to time-invariant systems, stationary signals, and noises. A stochastic integrodifferential equation is derived for the probability density of the state variables at time t conditioned upon the entire past history of the measurements up to time t. The solution of this equation yields the conditional probability density continuously in time. If the system under consideration is discrete in time, the corresponding conditional probability density is also discrete in time.

Nonlinear analysis of microwave FET oscillators using Volterra series

Abstract: A novel approach for determining the amplitude and frequency of nonlinear FET oscillators is presented. The nonlinear elements of the active device are modeled by the Volterra series method. The frequency and amplitude of oscillation are then calculated by solving two algebraic equations. Experimental results obtained from a constructed oscillator confirm the validity of the theory, the discrepancy between measured and calculated frequency and amplitude values being less than 10%. >

A general-purpose computer program for the Volterra-series analysis of nonlinear microwave circuits

Abstract: A computer program is described that performs a Volterra-series analysis of a weakly nonlinear microwave circuit having an arbitrary topology. The program uses the method of nonlinear currents and a nodal formulation. In this approach, each nonlinear circuit element is described as a linear element in parallel with a set of current sources; each current source represents a single order (greater than one) of the mixing products, and its current is a nonlinear function of the node-voltage components at lower-order mixing frequencies. The weakly nonlinear circuit is reduced to a linear circuit, which contains the linear elements and the linear parts of the nonlinear elements, and a set of excitation sources. The program is intended primarily for use in the design of microwave circuits; its catalog of circuit elements includes the distributed elements necessary for such work. Because the program formulates and solves the circuit equations numerically, the user need not simplify either the circuit or the model of the solid-state device, or make any of the other common simplifying assumptions. >

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.