Showing papers on "Volterra series published in 1967"

Transistor distortion analysis using volterra series representation

Abstract: Intermodulation distortion due to nonlinear elements in transistors is analyzed using Volterra series representation. It is shown that this technique is well suited for the analysis of transistor distortion where the nonlinearities are small but frequency dependent. An ac transistor model incorporating four nonlinearities is briefly described. The nonlinear nodal equations of the model are successively solved by expressing nodal voltages in terms of the Volterra series expansion of the input voltage. Based on this analysis, a digital computer program has been developed which computes the second and the third harmonic distortion for a given set of input frequencies and transistor parameters. The results compare favorably with measured values. This method also enables the derivation of closed form ac expressions for a simplified model; these expressions show the dependence of distortion on frequency, load and source impedances, bias currents and voltages, and the parameters of the transistor. The technique is also extended to cascaded transistors, and simplified expressions for the overall distortion in terms of the distortion and gain of individual transistors are derived. Finally, a few pertinent practical applications are discussed.

A learning technique for Volterra series representation

Abstract: This paper presents a method of system identification based upon the techniques of pattern recognition. The method developed is an on-line error-correcting procedure which provides the coefficients of the Volterra series representation of the system. The systems considered are those with finite settling time and piecewise constant inputs. The method is extremely general, identifying both linear and nonlinear systems in the presence of noise, without the requirement of special test signals. The theoretical basis for this method lies in the observation that system identification is a special case of the general theory of pattern recognition. A system is treated as a transformation from the set of past inputs to the real line, the system output. The Volterra expansion treats this transformation as a hypersurface, the shape of which is determined by the Volterra kernels. However, the techniques of pattern recognition produce this type of surface as the discriminant function between pattern classes. Furthermore, these surfaces are iteratively obtained as more data are available. Consequently, the computational difficulties, which are encountered in obtaining the Volterra kernels, are circumvented by this iterative learning procedure.

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.