Kernel-based modeling of dynamic systems has garnered a significant amount of attention in the system identification literature since its introduction to the field in [7]. While the method was originally applied to linear impulse response estimation in the time domain, the concepts have since been extended to the frequency domain for estimation of frequency response functions (FRFs) [6], as wel...

In this paper the solution of the Volterra integro-differential equations of fractional order is presented. The proposed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. We derive conditions under which the solution series, constructed by the method is convergent. Some examples are presented to verify convergen...

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

Volterra series is a powerful tool for blackbox macromodeling of nonlinear devices. However, the exponential complexity growth in storing and evaluating higher order Volterra kernels has limited so far its employment on complex practical applications. On the other hand, tensors are a higher order generalization of matrices that can naturally and efficiently capture multidimensional data. Signif...

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain...

This paper describes a method of implementing thermal power feedback (TPF) into a 5th order nonlinear distortion analysis with Volterra-series. The main advantages of the Volterra analysis is that diferent thermal and electrothermal contributions of distortion can be separated, giving extensive information about dominant distortion mechanisms. As an example, electro-thermal distortion in a simp...

Nonlinearity in evoked hemodynamic responses often presents in event-related fMRI studies. Volterra series, a higher-order extension of linear convolution, has been used in the literature to construct a nonlinear characterization of hemodynamic responses. Estimation of the Volterra kernel coefficients in these models is usually challenging due to the large number of parameters. We propose a new...

a method for solving a class of weakly singular volterra integral equations is given by using the fractional differential transform method. the approximate solution of these equa­tions is calculated in the form of a finite series with easily computable terms. while in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy an...

This paper presents a study aiming to define a nonlinear model, based on the Volterra series, of the high density optical disc read out process. I!nder high density condition, because of the high linear density and reduced track pitch, the signal read out is not a linear process and suffers from cross talk. To cope with such a problem the identification of a suitable nonlinear model is required...