Control System Analysis and Identification with MATLAB®

Block Pulse and Related Orthogonal Functions

Anish Deb, Srimanti Roychoudhury

• Publisher: CRC Press
• Year: 2018
• Print ISBN:
  9781138303225
• eBook ISBN:
  9781351399562
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Key Features:

• The Book Covers recent results of the traditional block pulse and other functions related material
• Discusses 'functions related to block pulse functions' extensively along with their applications
• Contains analysis and identification of linear time-invariant systems, scaled system, and sampled-data system
• Presents an overview of piecewise constant orthogonal functions starting from Haar to sample-and-hold function
• Includes examples and MATLAB codes with supporting numerical exampless.

1Block Pulse and Related Basis Functions

1.1Block Pulse and Related Basis Functions

Orthogonal properties [1] of familiar sine-cosine functions have been known for more than two centuries, but the use of such functions to solve complex analytical problems was initiated by the work of the famous mathematician Baron Jean-Baptiste-Joseph Fourier [2]. Fourier introduced the idea that an arbitrary function, even the one defined by different equations in adjacent segments of its range, could nevertheless be represented by a single analytic expression. Although this idea encountered resistance at the time, it proved to be pivotal to many later developments in many areas of mathematics, science, and engineering.

In many spheres of electrical engineering, the basis for any analysis is usually a system of sine-cosine functions. This is mainly due to the desirable properties of frequency domain representation of a large class of functions encountered in engineering design and also immense popularity of sinusoidal voltage in most engineering applications. In the fields of circuit analysis, control theory, communication, and analysis of stochastic problems, ample examples are found where the completeness and orthogonal properties [1] of such a system of sine-cosine functions lead to attractive solutions. But with the application of digital techniques in these areas, awareness for other more general complete systems of orthogonal functions has developed. This “new” class of functions, though not possessing so...

Table of contents

• Cover
• Half Title Page
• Title Page
• Copyright Page
• Dedication
• Contents
• List of Principal Symbols
• Preface
• Authors
• Chapter 1 Block Pulse and Related Basis Functions
• Chapter 2 Function Approximation via Block Pulse Function and Related Functions
• Chapter 3 Block Pulse Domain Operational Matrices for Integration and Differentiation
• Chapter 4 Operational Transfer Functions for System Analysis
• Chapter 5 System Analysis and Identification Using Convolution and “Deconvolution” in BPF Domain
• Chapter 6 Delayed Unit Step Functions (DUSF) for System Analysis and Fundamental Nature of the Block Pulse Function (BPF) Set
• Chapter 7 Sample-and-Hold Functions (SHFs) for System Analysis
• Chapter 8 Discrete Time System Analysis Using a Set of Delta Functions (DFs)
• Chapter 9 Non-Optimal Block Pulse Functions (NOBPFs) for System Analysis and Identification
• Chapter 10 System Analysis and Identification Using Linearly Pulse-Width Modulated Generalized Block Pulse Functions (LPWM-GBPF)
• Appendix A: Introduction to Linear Algebra
• Appendix B: Selected MATLAB Programs
• Index