Ideal Sequence Design in Time-Frequency Space: Applications to Radar, Sonar, and Communication Systems / Edition 1

by Myoung An, Andrzej K. Brodzik, Richard Tolimieri

Overview

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant devel- ments in harmonic analysis, ranging from abstract harmonic analysis to basic app- cations. The title of the series reffects 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 fields such as signal processing, partial differential equations (PDEs), and image processing is reffected 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.

Product Details

ISBN-13:	9780817647377
Publisher:	Birkhäuser Boston
Publication date:	12/02/2008
Series:	Applied and Numerical Harmonic Analysis
Edition description:	2009
Pages:	224
Product dimensions:	6.10(w) x 9.30(h) x 0.70(d)
Age Range:	3 Months

Table of Contents

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.- #x002A;-Permutations.- Permutation Sequences.- Modulation.- Sequence Sets.- Echo Analysis.- Sequence Shaping.- Problems.

Editorial Reviews

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)

From the Publisher