BOOK

## Triangular Orthogonal Functions for the Analysis of Continuous Time Systems

**Anish Deb** |
** Gautam Sarkar** |
** Anindita Sengupta**

(2011)

### Additional Information

#### Book Details

### Abstract

This book deals with a new set of triangular orthogonal functions, which evolved from the set of well-known block pulse functions (BPF), a major member of the piecewise constant orthogonal function (PCOF) family. Unlike PCOF, providing staircase solutions, this new set of triangular functions provides piecewise linear solution with less mean integral squared error (MISE).

After introducing the rich background of the PCOF family, which includes Walsh, block pulse and other related functions, fundamentals of the newly proposed set – such as basic properties, function approximation, integral operational metrics, etc. – are presented. This set has been used for integration of functions, analysis and synthesis of dynamic systems and solution of integral equations. The study ends with microprocessor based simulation of SISO control systems using sample-and-hold functions and Dirac delta functions.

Anish Deb is Professor at the Department of Applied Physics, University of Calcutta, India.

Gautam Sarkar is the Labonyamoyee Das Professor at the Department of Applied Physics, University of Calcutta, India.

Anindita Sengupta is Senior Lecturer at the Department of Electrical Engineering, Bengal Engineering and Science University, India.

"The book is readable for the interested mathematician and engineer"

—Jessica Steward Kelly, "Mathematical Review Clippings," July 2017.

This book deals with a new set of triangular orthogonal functions, which evolved from the set of well-known block pulse functions (BPF), a major member of the piecewise constant orthogonal function (PCOF) family. Unlike PCOF, providing staircase solutions, this new set of triangular functions provides piecewise linear solution with less mean integral squared error (MISE).

After introducing the rich background of PCOF family, which includes Walsh, block pulse and other related functions, fundamentals of the newly proposed set – such as basic properties, function approximation, integral operational metrics, etc. – are presented. This set has been used for integration of functions, analysis and synthesis of dynamic systems and solution of integral equations. The study ends with microprocessor based simulation of SISO control systems using sample-and-hold functions and Dirac delta functions.

### Table of Contents

Section Title | Page | Action | Price |
---|---|---|---|

FRONT MATTER | i | ||

Half Title Page | i | ||

About the Authors | ii | ||

Full Title Page | iii | ||

Copyright Page | iv | ||

Dedication | v | ||

Contents | vii | ||

Preface | xi | ||

MAIN MATTER | 1 | ||

Chapter 1: Walsh, Block Pulse, and Related Orthogonal Functions in Systems and Control | 1 | ||

Chapter 2: A Newly Proposed Triangular Function Set and Its Properties | 27 | ||

Chapter 3: Function Approximation via Triangular Function Sets and Operational Matrices in Triangular Function Domain | 59 | ||

Chapter 4: Analysis of Dynamic Systems via State Space Approach | 73 | ||

Chapter 5: Convolution Process in Triangular Function Domain and Its Use in SISO Control System Analysis | 83 | ||

Chapter 6: Identification of SISO Control Systems via State Space Approach | 101 | ||

Chapter 7: Solution of Integral Equations via Triangular Functions | 111 | ||

Chapter 8: Microprocessor Based Simulation of Control Systems Using Orthogonal Functions | 137 | ||

END MATTER | 153 | ||

Index | 153 |