Myoung An, Andrzej K. Brodzik, Richard Tolimieri

Ideal Sequence Design in Time-Frequency Space

Applications to Radar, Sonar, and Communication Systems

• Gebundenes Buch

Produktbeschreibung

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 inour 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.

Produktdetails

• Applied and Numerical Harmonic Analysis
• Verlag: Birkhäuser / Birkhäuser Boston / Springer, Basel
• Artikelnr. des Verlages: 12084975, 978-0-8176-4737-7
• 2009 edition
• Seitenzahl: 224
• Erscheinungstermin: 2. Dezember 2008
• Englisch
• Abmessung: 243mm x 162mm x 15mm
• Gewicht: 478g
• ISBN-13: 9780817647377
• ISBN-10: 0817647376
• Artikelnr.: 23100633

Inhaltsangabe

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.

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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.

Rezensionen

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)