'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y se.rais point aile.' human race. It has put common sense back Jules Verne where it belongs, on!be topmost shelf next to the dusty canister labelled 'disc:arded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

This book provides a broadly based, theoretical monograph on the Walsh System, a system that is the simplest non-trivial model for harmonic analysis and shares many properties with the trigonometric system. It gives a thorough introduction to foundations of Walsh-Fourier analysis introducing the main techniques and fundamental problems in a way that makes the literature accessible. It also shows how the theory of Walsh-Fourier analysis relates to other aspects of harmonic analysis. The book will be of interest to postgraduate students in pure and applied mathematics, and those studying numerical analysis and computational mathematics.

This book is intended for those wishing to acquire a working knowledge of orthogonal transforms in the area of digital signal processing. The authors hope that their introduction will enhance the opportunities for interdiscipli nary work in this field. The book consists of ten chapters. The first seven chapters are devoted to the study of the background, motivation and development of orthogonal transforms, the prerequisites for which are a basic knowledge of Fourier series transform (e.g., via a course in differential equations) and matrix al gebra. The last three chapters are relatively specialized in that they are di rected toward certain applications of orthogonal transforms in digital signal processing. As such, a knowlegde of discrete probability theory is an essential additional prerequisite. A basic knowledge of communication theory would be helpful, although not essential. Much of the material presented here has evolved from graduate level courses offered by the Departments of Electrical Engineering at Kansas State University and the University of Texas at Arlington, during the past five years. With advanced graduate students, all the material was covered in one semester. In the case of first year graduate students, the material in the first seven chapters was covered in one semester. This was followed by a prob lems project-oriented course directed toward specific applications, using the material in the last three chapters as a basis.

Boolean functions are the building blocks of symmetric cryptographic systems. Symmetrical cryptographic algorithms are fundamental tools in the design of all types of digital security systems (i.e. communications, financial and e-commerce).Cryptographic Boolean Functions and Applications is a concise reference that shows how Boolean functions are used in cryptography. Currently, practitioners who need to apply Boolean functions in the design of cryptographic algorithms and protocols need to patch together needed information from a variety of resources (books, journal articles and other sources). This book compiles the key essential information in one easy to use, step-by-step reference. Beginning with the basics of the necessary theory the book goes on to examine more technical topics, some of which are at the frontier of current research. Serves as a complete resource for the successful design or implementation of cryptographic algorithms or protocols using Boolean functions Provides engineers and scientists with a needed reference for the use of Boolean functions in cryptography Addresses the issues of cryptographic Boolean functions theory and applications in one concentrated resource Organized logically to help the reader easily understand the topic

Signals, Systems, Transforms, and Digital Signal Processing with MATLAB® has as its principal objective simplification without compromise of rigor. Graphics, called by the author, "the language of scientists and engineers", physical interpretation of subtle mathematical concepts, and a gradual transition from basic to more advanced topics are meant to be among the important contributions of this book. After illustrating the analysis of a function through a step-by-step addition of harmonics, the book deals with Fourier and Laplace transforms. It then covers discrete time signals and systems, the z-transform, continuous- and discrete-time filters, active and passive filters, lattice filters, and continuous- and discrete-time state space models. The author goes on to discuss the Fourier transform of sequences, the discrete Fourier transform, and the fast Fourier transform, followed by Fourier-, Laplace, and z-related transforms, including Walsh–Hadamard, generalized Walsh, Hilbert, discrete cosine, Hartley, Hankel, Mellin, fractional Fourier, and wavelet. He also surveys the architecture and design of digital signal processors, computer architecture, logic design of sequential circuits, and random signals. He concludes with simplifying and demystifying the vital subject of distribution theory. Drawing on much of the author’s own research work, this book expands the domains of existence of the most important transforms and thus opens the door to a new world of applications using novel, powerful mathematical tools.

Signals and Transforms in Linear Systems Analysis covers the subject of signals and transforms, particularly in the context of linear systems theory. Chapter 2 provides the theoretical background for the remainder of the text. Chapter 3 treats Fourier series and integrals. Particular attention is paid to convergence properties at step discontinuities. This includes the Gibbs phenomenon and its amelioration via the Fejer summation techniques. Special topics include modulation and analytic signal representation, Fourier transforms and analytic function theory, time-frequency analysis and frequency dispersion. Fundamentals of linear system theory for LTI analogue systems, with a brief account of time-varying systems, are covered in Chapter 4 . Discrete systems are covered in Chapters 6 and 7. The Laplace transform treatment in Chapter 5 relies heavily on analytic function theory as does Chapter 8 on Z -transforms. The necessary background on complex variables is provided in Appendix A. This book is intended to serve as a text on signals and transforms for a first year one semester graduate course, primarily for electrical engineers.

This book presents an overview of political economic change in Vietnam during a period of significant social and economic change and an era of international turbulence. It combines various political economic perspectives to offer an integrated and comprehensive review of Vietnam’s recent development, discussing topics such as public administrative reform, labour markets and special economic zones, environmental management and other important contemporary issues. This concise and highly readable book includes a considerable amount of research, and as such provides valuable insights for scholars and researchers interested in political economic change and in Vietnam.

This book has grown from notes used by the authors to instruct fast transform classes. One class was sponsored by the Training Department of Rockwell International, and another was sponsored by the Department of Electrical Engineering of The University of Texas at Arlington. Some of the material was also used in a short course sponsored by the University of Southern California. The authors are indebted to their students for motivating the writing of this book and for suggestions to improve it.

The Laplace Transform is used to solve initial value problems involving differential equations. All steps included. Conventional methods are also discussed.