Journal ArticleDOI
A new set of orthogonal functions and its application to the analysis of dynamic systems
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TLDR
It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.Abstract:
The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.read more
Citations
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Triangular functions based method for the solution of system of linear Fredholm integral equations via an efficient finite iterative algorithm
Journal ArticleDOI
One- and two-dimensional scattering analysis using a fast numerical method
TL;DR: This study presents a fast numerical method based on vector forms for representation of triangular functions that reduces to solving a linear system of algebraic equations of large condition number for solving integral equations of the first kind.
Journal ArticleDOI
Analysis and synthesis of time-varying systems via orthogonal hybrid functions (HF) in state space environment
TL;DR: In this paper, a set of hybrid functions (HF) formed by a combination of sample-and-hold function (SHF) set and triangular function (TF) set is used for time-varying system analysis.
Journal Article
Numerical Solution of Second Kind Volterra and Fredholm Integral Equations Based on a Direct Method Via Triangular Functions
TL;DR: In this article, a numerical method for solving linear integral equations of the second kind is formulated based on a special representation of vector forms of triangular functions and the related operational matrix of integration.
Proceedings ArticleDOI
Method of approximation functions for solution of 2D nonlinear volterra integral equation
D. Zolotariov,A. Nerukh +1 more
TL;DR: In this article, the approximation functions method for solution of an integral equation is considered and a non-linear 2D Volterra integral equation which describes electromagnetic wave propagation in a nonlinear layer is solved by this method.
References
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Zur Theorie der orthogonalen Funktionensysteme
TL;DR: In der Theorie der Reihenentwicklung der reellen Funktionen spielen die sog. orthogonalen Funktionensysteme eine fuhrende Rolle.
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Identification of continuous-time systems
G.P. Rao,Heinz Unbehauen +1 more
TL;DR: Continuous-time model-based system identification as mentioned in this paper is a well-established field in the field of control systems and is concerned with the determination of particular models for systems that are intended for a certain purpose such as control.
Journal ArticleDOI
Walsh operational matrices for fractional calculus and their application to distributed systems
C.F. Cheng,Y.T. Tsay,Tao Wu +2 more
TL;DR: In this paper, the Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems and a new set of orthogonal functions is derived from Walsh functions.