The performance of linear acoustic echo cancelers degrades if nonnegligible nonlinear distortion is introduced into the echo path as, e.g., caused by low-cost loudspeaker systems driven at high volume. Adaptive second-order Volterra filters are known to effectively model nonlinear acoustic echo paths. In this contribution we propose an extension of the proportionate NLMS (PNLMS) to second-order...

Considered as a prototype of nonlinear system models the second order Volterra filter (FV2) is characterized by an increased complexity in comparison with a linear filter. This complexity is given by the large number of filter coefficients, as well as by the filter operations and it requires an increased computational power in technical applications. The filter based on the multi memory decompo...

Providing flexibility and user-interpretability in nonlinear system identification can be achieved by means of block-oriented methods. One of such block-oriented system structures is the parallel WienerHammerstein system, which is a sum of Wiener-Hammerstein branches, consisting of static nonlinearities sandwiched between linear dynamical blocks. Parallel Wiener-Hammerstein models have more des...

In this paper, we are to develop a second-order LMS-type adaptive equalizer to reduce distortions of data transmission over analog telephone channels due the channel impulse response and inter-symbol interference (ISI). A novel approach for updating the linear and quadratic coefficients vectors of a second-order Volterra filter is presented. The innovative features of this algorithm provide dis...

More than 20 years ago it was shown that adaptive Volterra filters can be used for telephone echo cancellation, but the inherent need for a large number of coefficients has inhibited their practical use. Recently, first attempts have been made to combat nonlinearities in the acoustic echo path of hands-free telephones, which are caused by low-cost audio components. As these attempts are based o...

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations ...

The paper concerns studies the stochastic stability and stochastic asymptotic stability of the equilibrium solution of a nonlinear Volterra difference equation which is subject to stochastic state independent disturbances. It is shown that if the linearized deterministic equation has summable solutions, then the nonlinear stochastic equation will be stable or asymptotically stable, provided tha...

This paper proposes the use of a class of feedforward artificial neural networks with polynomial activation functions (distinct for each hidden unit) for practical modeling of high-order Volterra systems. Discrete-time Volterra models (DVMs) are often used in the study of nonlinear physical and physiological systems using stimulus-response data. However, their practical use has been hindered by...