The Mathematics of Signal Processing

Erscheinungsjahr 2011
ISBN: 978-1-107-60104-8
Verlag: Cambridge University Press

Buch, Englisch, Band 48, 462 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 744 g

Reihe: Cambridge Texts in Applied Mathematics

Arising from courses taught by the authors, this largely self-contained treatment is ideal for mathematicians who are interested in applications or for students from applied fields who want to understand the mathematics behind their subject. Early chapters cover Fourier analysis, functional analysis, probability and linear algebra, all of which have been chosen to prepare the reader for the applications to come. The book includes rigorous proofs of core results in compressive sensing and wavelet convergence. Fundamental is the treatment of the linear system y=Fx in both finite and infinite dimensions. There are three possibilities: the system is determined, overdetermined or underdetermined, each with different aspects. The authors assume only basic familiarity with advanced calculus, linear algebra and matrix theory and modest familiarity with signal processing, so the book is accessible to students from the advanced undergraduate level. Many exercises are also included.

Autoren/Hrsg.

Damelin, Steven B.

Miller, Jr Willard

Fachgebiete

• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Signalverarbeitung
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

1. Introduction; 2. Normed vector spaces; 3. Analytic tools; 4. Fourier series; 5. Fourier transforms; 6. Compressive sensing; 7. Discrete transforms; 8. Linear filters; 9. Windowed Fourier transforms, continuous wavelets, frames; 10. Multiresolution analysis; 11. Discrete wavelet theory; 12. Biorthogonal filters and wavelets; 13. Parsimonious representation of data; Bibliography; Index.

Über Autor(innen)

Miller, Jr Willard
Willard Miller, Jr is Professor Emeritus in the School of Mathematics at the University of Minnesota.

Damelin, Steven B.
Steven B. Damelin is currently Full Professor at Georgia Southern University and Visiting Full Professor at the University of the Witwatersrand in Johannesburg.