Discrete Fractional Calculus: Applications In Control And Image Processing

by Piotr Ostalczyk

Overview

The main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward difference and sum. In the second part, selected applications of the discrete fractional calculus in the discrete system control theory are presented. In the discrete system identification, analysis and synthesis, one can consider integer or fractional models based on the fractional-order difference equations. The third part of the book is devoted to digital image processing.

Product Details

ISBN-13:	9789814725668
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	01/28/2016
Series:	Series In Computer Vision , #4
Pages:	396
Product dimensions:	6.50(w) x 9.80(h) x 1.00(d)

Table of Contents

Discrete-Variable Real Functions; The n-th Order Backward Difference/Sum of the Discrete-Variable Function; Fractional-Order Backward Differ-Sum; The FOBD-S Graphical Interpretation; The FOBD/S Selected Properties; The FO Dynamic System Description; Linear FO System Analysis; The Linear FO Discrete-Time Fundamental Elements; FO Discrete-Time System Structures; Fractional Discrete-Time PID Controller; FOS Approximation Problems; Fractional Potential; FO Image Filtering and Edge Detection; Appendix A: Selected Linear Algebra Formulae and Discrete-Variable Special Functions;