Ideal Sequence Design in Time-Frequency Space: Applications to Radar, Sonar, and Communication Systems

ISBN-13: 9780817647377 / Angielski / Twarda / 2008 / 224 str.

Myoung An; Andrzej K. Brodzik; Richard Tolimieri

Opis

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?c communities with signi?cant devel- ments in harmonic analysis, ranging from abstract harmonic analysis to basic app- cations. The title of the series re?ects the importance of applications and numerical implementation, but richness and relevance of applications and implementation - pend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbiotic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has ?ourished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship - tween harmonic analysis and ?elds such as signal processing, partial differential equations (PDEs), and image processing is re?ected in our state-of-the-art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time-frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.

Recenzje

From the reviews:

"The book ... develops a new theory leading to systematic sequence design in time-frequency space. The essential tool of this interesting method is the finite Zak transform, which provides sparse representations for the discrete Fourier transform, cyclic convolution, and correlation. Using this Zak representation, the authors construct a large class of sequence sets satisfying pairwise ideal correlation. ... This interesting and well-written book will be a useful reference text for graduate students, researchers, and engineers interested in radar/sonar signal processing or communication systems." (Manfred Tasche, Zentralblatt MATH, Vol. 1160, 2009)

Spis treści

ANHA Series Preface Preface Introduction Review of Algebra Permutations and Permutation Matrices Finite Fourier Transform Convolution and Correlation Discrete Chirps Zak Transform Zak Space Correlation Formula Zak Space Representation of Chirps *-Permutations Permutation Sequences Modulation Sequence Sets Echo Analysis Sequence Shaping Problems References Index

Blurb

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.