Journal ArticleDOI
Block pulse functions, the most fundamental of all piecewise constant basis functions
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TLDR
In this article, it is shown that block pulse functions (BPFs) are superior to the delayed unit step function (DUSF) proposed by Hwang (1983) due to the most elemental nature of BPFs in comparison to any other PCBF function.Abstract:
It is established that block pulse functions (BPFs) are superior to the delayed unit step function (DUSF) proposed by Hwang (1983). The superiority is mainly due to the most elemental nature of BPFs in comparison to any other PCBF function. It is also proved that the operational matrix for integration in the BPF domain is connected to the integration operational matrix in the DUSF domain by simple linear transformation involving invertible Toeplitz matrices. The transformation appears to be transparent because the integration operational matrices are found to match exactly. The reason for such transparency is explained mathematically. Finally, Hwang claimed superiority of DUSFs compared to Walsh functions in obtaining the solution of functional differential equations using a stretch matrix in the DUSF domain. It is shown that the stretch matrices of Walsh and DUSF domains are also related by linear transformation and use of any of these two matrices leads to exactly the same result. This is supported by a...read more
Citations
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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 ArticleDOI
On Walsh/block pulse domain analysis of power electronic circuits Part 1. Continuously phase-controlled rectifier
Anish Deb,Asit K. Datta +1 more
TL;DR: In this article, a Walsh operational transfer function (WOTF) is utilized instead of a conventional transfer function to obtain the output response, e.g. average and r.m.s.
Journal ArticleDOI
Numerical instability of deconvolution operation via block pulse functions
TL;DR: This paper characterizes oscillations found in block pulse function (BPF) domain identification of open loop first-order systems with step input by presenting a useful condition for occurrence of such oscillations.
Journal ArticleDOI
Optimal Selection of Basis Functions for Robust Tracking Control of Uncertain Linear Systems—With Application to Three-Dimensional Printing
TL;DR: In this paper, the effect of the choice of the basis functions on the tracking accuracy of FBF, in the presence of uncertainties, using the Frobenius norm of the lifted system representation (LSR) of the FBF's error dynamics is analyzed.
Journal ArticleDOI
On improvement of the integral operational matrix in block pulse function analysis
TL;DR: In this paper, Chen and Chung (1987) showed that the trapezoidal rule is equivalent to evaluating the BPF coefficients of the integrated function by the well known trapezoid rule.
References
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Book
Transmission of information by orthogonal functions
Henning F. Harmuth,Joseph D. Lee +1 more
TL;DR: When you read more every page of this transmission of information by orthogonal functions, what you will obtain is something great.
Journal ArticleDOI
On a Functional Differential Equation
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.
Book
Piecewise Constant Orthogonal Functions and Their Application to Systems and Control
TL;DR: In this article, the authors proposed piecewise constant orthogonal basis functions (PCF) for linear and non-linear linear systems, and the optimal control of linear lag-free and time-lag systems.
Journal ArticleDOI
Analysis and synthesis of dynamic systems via block-pulse functions
TL;DR: The paper presents a method of numerically integrating a system of differential equations based on an idea of orthogonal approximation of functions that gives piecewise constant solutions with minimal mean-square error and is computationally similar to the familiar trapezoidal rule of integration.
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