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Sequency theory --- Signal processing --- Walsh functions

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Dyadic (Walsh) analysis emerged as a new research area in applied mathematics and engineering in early seventies within attempts to provide answers to demands from practice related to application of spectral analysis of different classes of signals, including audio, video, sonar, and radar signals. In the meantime, it evolved in a mature mathematical discipline with fundamental results and important features providing basis for various applications. The book will provide fundamentals of the area through reprinting carefully selected earlier publications followed by  overview of recent results concerning particular subjects in the area written by experts, most of them being founders of the field, and some of their followers. In this way, this first volume of the two volume book offers a rather complete coverage of the development of dyadic Walsh analysis, and provides a deep insight into its mathematical foundations necessary for consideration of generalizations and applications that are the subject of the second volume. The presented theory is quite sufficient to be a basis for further research in the subject area as well as to be applied in solving certain new problems or improving existing solutions for tasks in the areas which motivated development of the dyadic analysis.

Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Walsh functions. --- Harmonic analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Functions, Walsh --- Mathematics. --- Computer science --- Abstract Harmonic Analysis. --- Math Applications in Computer Science. --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Functions, Orthogonal --- Sequency theory

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517.518.5 --- Fourier analysis --- Harmonic analysis --- Mathematical physics --- Walsh functions --- Functions, Walsh --- Functions, Orthogonal --- Sequency theory --- Physical mathematics --- Physics --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Analysis, Fourier --- Theory of the Fourier integral --- 517.518.5 Theory of the Fourier integral

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This self-contained book develops theory and algorithms leading to systematic sequence design in time-frequency space. The primary tool used is the Zak transform, which provides sparse representation for the Fourier transform, convolution, and correlation. Using this multi-dimensional representation, the authors construct a large class of sequence sets satisfying pairwise ideal correlation. The complex algebraic analysis of sequences is replaced by an elegant and efficient geometric analysis of images, whose advantage is realized as an N to N! increase in the number of ideal sequence sets. Topics and features: * Mathematical development of the theory is illustrated with many examples. * Standard communication theory and Zak space methods are numerically compared. * Application areas covered include pulse radar and sonar, multi-beam radar and sonar imaging systems, remote identification of dielectrics, and code division multiple-access communication. * Background is provided in two introductory chapters on matrix algebra, tensor products, and permutation groups. * A list of open problems is presented and directions for further research are discussed. Ideal Sequence Design in Time-Frequency Space is an excellent reference text for graduate students, researchers, and engineers interested in radar, sonar, and communication systems. The work may also be used as a supplementary textbook for a graduate course or seminar on sequence design in time-frequency space.

Fourier transformations. --- Frequencies of oscillating systems. --- Radar. --- Sequency theory. --- Sonar. --- Telecommunication systems --Design and construction. --- Sequency theory --- Fourier transformations --- Frequencies of oscillating systems --- Radar --- Sonar --- Telecommunication systems --- Telecommunications --- Electrical & Computer Engineering --- Engineering & Applied Sciences --- Design and construction --- Asdic --- Echo ranging --- Sound navigation ranging --- Frequencies of vibrating systems --- Frequency analysis (Dynamics) --- Frequency of oscillation --- Frequency of vibration --- Vibration frequencies --- Transformations, Fourier --- Transforms, Fourier --- Design and construction. --- Engineering. --- Harmonic analysis. --- Fourier analysis. --- Applied mathematics. --- Engineering mathematics. --- Algorithms. --- Electrical engineering. --- Signal, Image and Speech Processing. --- Fourier Analysis. --- Communications Engineering, Networks. --- Applications of Mathematics. --- Abstract Harmonic Analysis. --- Detectors --- Electronics in navigation --- Signals and signaling, Submarine --- Ultrasonic equipment --- Underwater acoustics --- Electronic systems --- Pulse techniques (Electronics) --- Radio --- Remote sensing --- Oscillations --- Vibration --- Fourier analysis --- Transformations (Mathematics) --- Signal theory (Telecommunication) --- Telecommunication --- Walsh functions --- Telecommunication. --- Mathematics. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Math --- Science --- Electric communication --- Mass communication --- Telecom --- Telecommunication industry --- Communication --- Information theory --- Telecommuting --- Algorism --- Algebra --- Arithmetic --- Analysis, Fourier --- Foundations --- Signal processing. --- Image processing. --- Speech processing systems. --- Engineering --- Engineering analysis --- Electric engineering --- Computational linguistics --- Modulation theory --- Oral communication --- Speech --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement