1.

Record Nr.

UNINA9910452993003321

Autore

Damelin Steven B.

Titolo

The mathematics of signal processing / / Steven B. Damelin, Willard Miller, Jr [[electronic resource]]

Pubbl/distr/stampa

Cambridge : , : Cambridge University Press, , 2012

ISBN

1-107-22943-X

1-280-77480-0

1-139-22281-3

9786613685193

1-139-22452-2

1-139-21801-8

1-139-00389-5

1-139-21492-6

Descrizione fisica

1 online resource (xii, 449 pages) : digital, PDF file(s)

Collana

Cambridge texts in applied mathematics ; ; 48

Disciplina

621.38220151

Soggetti

Signal processing - Mathematics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Nota di bibliografia

Includes bibliographical references (p. [437]-442) and index.

Nota di contenuto

Preface -- Introduction -- 1. Normed vector spaces -- 2. Analytic tools -- 3. Fourier series -- 4. The Fourier transform -- 5. Compressive sampling -- 6. Discrete transforms -- 7. Linear filters -- 8. Windowed fourier and continuous wavelet transforms. Frames -- 9. Multiresolution analysis -- 10. Discrete wavelet theory -- 11. Biorthogonal filters and wavelets -- 12. Parsimonious representation of data.

Sommario/riassunto

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=Φx 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.