The present work proposes a significant modification to conventional block pulse functions (BPF) by describing a novel set of pulse-width modulated generalized block pulse functions (PWM-GBPF) which has been utilized to develop generalized correlation matrices of operational nature. These matrices are used to determine cross-/auto-correlation of time-varying functions. Numerical examples are treated to establish the validity of the proposal. Also, a representational error analysis has been carried out for the PWM-GBPF to show that this kind of BPF set introduces a smaller error than the conventional equal width BPF. © 1995 Taylor & Francis Group, LLC.

A DEB

G SARKAR

S K SEN

A K DATTA

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

A new set of pulse-width modulated generalized block pulse functions (PWM-GBPF) and its application to cross-/auto-correlation of time-varying functions

International Journal of Systems Science

This chapter discusses different types of non-sinusoidal orthogonal functions such as Haar functions, Walsh functions, block pulse functions, sample-and-hold functions, triangular functions, non-optimal block pulse functions and a few others. It also discusses briefly the application of Walsh, block pulse and triangular functions, three major members of the non-sinusoidal orthogonal function family, in the area of systems and control. Finally, this chapter proposes a new set of orthogonal functions named ‘Hybrid Function’ (HF). At the end of the chapter, more than hundred useful references are given. © Springer International Publishing Switzerland 2016.

Studies in Systems, Decision and Control

Non-sinusoidal orthogonal functions in systems and control

The present work makes use of the block pulse domain operational matrix for differentiation D1(m) to find out an operational transfer function. Analysis of simple control systems using this Block Pulse Operational Transfer Function (BPOTF) shows that the results are not so accurate when compared with the direct expansion of the exact solution in the BPF domain. To remove this defect, one shot operational matrices for repeated integration (OSOMRI) are obtained and these matrices are used to develop a Modified Block Pulse Operational Transfer Function (MBPOTF) for linear SISO control system analysis in the block pulse function domain. A few linear SISO control systems are analysed using the developed MBPOTFs as illustrative examples. The results are found to match exactly with the direct BPF expansions of the exact solutions. Copyright © 1997 Published by Elsevier Science Ltd.

Journal of the Franklin Institute

All-integrator approach to linear SISO control system analysis using Block Pulse Functions (BPF)

The paper presents a computational technique through operational matrices using a set of mutually disjoint delta functions (DF) for the analysis of linear discrete control systems. Following a brief review of the well known block pulse functions (BPF), a new set of delta functions is viewed in the same light. This set is used to develop operational transfer functions in the delta function domain (DOTF) and employed for discrete system analysis which results in the same accuracy as the conventional z-transform method. The presented technique uses simple matrix manipulations and is able to do away with laborious and involved algebraic steps, including inverse transformation, associated with the z-transform analysis without losing accuracy. Also, the accuracy of sample values of the output does not depend upon m (or the sampling interval h). A few linear discrete SISO control systems, open loop as well as closed loop, having different typical plant transfer functions, are analysed as illustrative examples. © lEE, 1996.

IEE Proceedings: Control Theory and Applications

Analysis of linear discrete SISO control systems via a set of delta functions

Application of a generalized block pulse function to a scaled system

On the operational matrices of block pulse functions

Signal Processing

Applications of walsh and related functions. With an introduction to sequence theory

Lecture Notes in Control and Information Sciences

Piecewise Constant Orthogonal Functions and Their Application to Systems and Control

Walsh Operational Matrices for Fractional Calculus and Their Application to Distributed Systems

Journal	International Journal of Systems Science
Publisher	-
ISSN	0020-7721