Volterra and Wiener series

Nonlinear prediction of speech signal using volterra-wiener series

Linear Prediction (LP) analysis has proven to be very effective and successful in speech analysis and speech synthesis applications. This may be due to the fact that LP analysis captures implicitly the time-varying vocal tract area function. However, it captures only the second-order statistical relationships and only the linear dependencies in the sequence of samples of speech signals (and not...

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 ...

Volterra and Fliess Series Expansion

Implicit Wiener Series

The Wiener series is one of the standard methods to systematically characterize the nonlinearity of a neural system. The classical estimation method of the expansion coefficients via cross-correlation suffers from severe problems that prevent its application to high-dimensional and strongly nonlinear systems. We propose a new estimation method based on regression in a reproducing kernel Hilbert...