Transmission of Information by Orthogonal Functions

Transmission of Information by Orthogonal Functions PDF

Author: Henning F. Harmuth

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 335

ISBN-13: 3662132273

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The orthogonality of functions has been exploited in communications since its very beginning. Conscious and 1 extensive use was made of it by KOTEL NIKOV in theoretical work in 1947. Ten years later a considerable number of people were working in this field rather independently. However, little experimental use could be made of the theo retical results before the arrival of solid state opera tional amplifiers and integrated circuits. A theory of communication based on orthogonal functions could ·have been published many years ago. However, the only useful examples of orthogonal functions at that time were sine .... cosine functions and block pulses, and this made the theory appear to be a complicated way to derive known re sults. It was again the advance of semiconductor techno logy that produced the first really new, useful example of orthogonal functions: the little-known Walsh functions. In this book emphasis is placed on the Walsh functions, since ample literature is available on sine-cosine func tions as well as on block pulses and pulses derived from them.

Triangular Orthogonal Functions for the Analysis of Continuous Time Systems

Triangular Orthogonal Functions for the Analysis of Continuous Time Systems PDF

Author: Anīśa Deba

Publisher: Anthem Press

Published: 2011

Total Pages: 169

ISBN-13: 0857289993

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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 family (PCOF). 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. This book is a source of new knowledge to researchers and academicians in the area of mathematics as well as systems and control.

Fourier Series and Orthogonal Functions

Fourier Series and Orthogonal Functions PDF

Author: Harry F. Davis

Publisher: Courier Corporation

Published: 2012-09-05

Total Pages: 436

ISBN-13: 0486140733

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This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging. The first three chapters of the book address linear spaces, orthogonal functions, and the Fourier series. Chapter 4 introduces Legendre polynomials and Bessel functions, and Chapter 5 takes up heat and temperature. The concluding Chapter 6 explores waves and vibrations and harmonic analysis. Several topics not usually found in undergraduate texts are included, among them summability theory, generalized functions, and spherical harmonics. Throughout the text are 570 exercises devised to encourage students to review what has been read and to apply the theory to specific problems. Those preparing for further study in functional analysis, abstract harmonic analysis, and quantum mechanics will find this book especially valuable for the rigorous preparation it provides. Professional engineers, physicists, and mathematicians seeking to extend their mathematical horizons will find it an invaluable reference as well.

Image Encryption

Image Encryption PDF

Author: Fathi E. Abd El-Samie

Publisher: CRC Press

Published: 2013-12-14

Total Pages: 406

ISBN-13: 1466576995

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Investigating image encryption approaches, this book examines image encryption algorithms for the purpose of wireless communication of images in secure form. It considers two directions for image encryption: permutation-based encryption and diffusion-based encryption. Covering the range of image encryption principles and techniques, it presents hybrid encryption algorithms to enhance the characteristics of traditional algorithms. It explores number theory-based encryption algorithms, details the strength of different encryption algorithms, and describes their ability to work within the limitations of wireless communication systems.

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