Rationalized Haar functions are developed to approximate the solution of the nonlinear Volterra–Fredholm–Hammerstein integral equations. The properties of rationalized Haar functions are first presented. These properties together with the Newton–Cotes nodes and Newton–Cotes integration method are then utilized to reduce the solution of Volterra–Fredholm–Hammerstein integral equations to the sol...

This paper presents a novel parallel recursive least squares (RLS) second-order adaptive Volterra filter (PAVF) to alleviate computational work. The adaptive Volterra filter (AVF) corresponding to the nonlinear characteristics is attractive due to the linear relationship between its input and output signals [1]. However, the extensive computational work of AVF limits its practical use, particul...

The main purpose of this article is to demonstrate the use of the two Dimensional Walsh and Haar functions with Operational Matrix for solving nonlinear Volterra-Fredholm integral equations. The approximate solution is represented in the form of series. The approximate solution is obtained by two Dimensional Walsh and Haar series. The operational matrix and direct method for solving the linear ...

A diagonal coordinate representation for Volterra filters is developed and exploited to derive efficient Volterra filter implementations for processing carrier based input signals. In the diagonal coordinate representation the output is expressed as a sum of linear filters applied to modified input signals. Hence, linear filtering methods are employed to implement the nonlinear filter on a base...

This paper exhibits an algorithm based on Volterra-type processing in order to detect several independent sources on the same carrier frequency and to determine the number of them. The use of infinite impulse ratio (IIR) Volterra filtering to build a suitable discrimination test is dictated by the need of higher-order moments in this type of nonlinear problem, as well as the need of IIR for con...

we reduce the two phase stefan problem with kinetic to a system of nonlinear volterra integral equations of second kind and apply newton's method to linearize it. we found product integration solution of the linear form. sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with an example.

Abstract. In this paper, a method is employed to approximate the solution of two-dimensional nonlinear Volterra integro-differential equations (2DNVIDEs) with supplementary conditions. First, we introduce twodimensional Legendre polynomials, then convert 2DNVIDEs to the two-dimensional linear Volterra integrodifferential equations (2DLVIDEs). Using this properties and collocation points, reduce...

The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to quantum estimation and detection based on Volterra filters. Volterra filters have a clear hierarchy of computational complexities and performances, depend onl...

The adaptive Volterra filter (AVF) corresponding to nonlinear system is attractive due to its linear relationship between the input and output signals. However, the formidable computer complexity of AVF is prohibitive for its practical applications. This paper presents a design method of noise canceller by using a parallel fast recursive least squares (RLS) adaptive Volterra filter (PAVF). PAVF...