On Modelling AM/AM and AM/PM Conversions via Volterra Series

On Modelling of Nonlinear Systems and Phenomena with the Use of Volterra and Wiener Series

This is a short tutorial on Volterra and Wiener series applications to modelling of nonlinear systems and phenomena, and also a survey of the recent achievements in this area. In particular, we show here how the philosophies standing behind each of the above theories differ from each other. On the other hand, we discuss also mathematical relationships between Volterra and Wiener ker...

Volterra Series and Permutation Groups

shuffle product of the permutations u E E k and v' E E k, we mean the following element from ~+~, /,, (i), i < k , vmv'=: Z o'o(~,| where (v~v') ( i ) = ~ . v , ( i _ k ) + l e ' i ' > k . a(~sk+n'cn} Since the permutations form an additive basis of the space ~ , the shuffle multiplication is uniquely extended "by linearity" to any pair of elements from ~ and defines in $ = ~0$n a structure of ...

On series solutions of Volterra equations

We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also obtain solutions to certain systems of Volterra equations of the first kind. In all cases except the case of logarithmic singularities, we obtain recursive fo...

Volterra and Fliess Series Expansion

On Selection of Test Disturbances While Modelling the Non-linear Dynamic Systems by Volterra Series

Perspectiveness of the Volterra series is determined by an e±cient solution to the problem of the model "adjustment" to the concrete object, i.e. a typical inverse identi ̄cation problem of the Volterra kernels by system responses to some test input disturbances. The approach known in the identi ̄cation theory that is based on introduction of test pulse-type disturbances turns out to be inapplica...