Pierre Bremaud

Mathematical Principles of Signal Processing

Fourier and Wavelet Analysis

• Broschiertes Buch

Produktbeschreibung

Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research.
This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals.
The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling,filtering, digital signal processing. Fourier analysis in Hilbert spaces is the focus of the third part, and the last part provides an introduction to wavelet analysis, time-frequency issues, and multiresolution analysis. An appendix provides the necessary background on Lebesgue integrals.

Produktdetails

• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4419-2956-3
• Softcover reprint of hardcover 1st ed. 2002
• Seitenzahl: 284
• Erscheinungstermin: 3. Dezember 2010
• Englisch
• Abmessung: 235mm x 155mm x 16mm
• Gewicht: 435g
• ISBN-13: 9781441929563
• ISBN-10: 1441929568
• Artikelnr.: 32181799

Autorenporträt

Fourier analysis and its modern extension of wavelet analysis provides one of the most useful tools in many applied sciences. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction to the subject, while emphasizing their uses in signal processing and other applications in communications engineering. An appendix provides the necessary background on Lebesgue integrals.

Inhaltsangabe

A1 Fourier Transforms of Stable Signals.- A2 Fourier Series of Locally Stable Periodic Signals.- A3 Pointwise Convergence of Fourier Series.- B1 Filtering.- B2 Sampling.- B3 Digital Signal Processing.- B4 Subband Coding.- C1 Hilbert Spaces.- C2 Complete Orthonormal Systems.- C3 Fourier Transforms of Finite-Energy Signals.- C4 Fourier Series of Finite-Power Periodic Signals.- D1 The Windowed Fourier Transform.- D2 The Wavelet Transform.- D3 Wavelet Orthonormal Expansions.- D4 Construction of an MRA.- D5 Smooth Multiresolution Analysis.- The Lebesgue Integral.- References.- Glossary of Symbols.

Rezensionen

From the reviews: MATHEMATICAL REVIEWS "While many books exits, dealing either with theory or applications, the interplay between signal processing and mathematics makes it difficult to find in a single volume the essentials of modern signal processing presented in a way which would be both rigorous for mathematicians and accessible for engineers. This challenge is precisely the purpose of Bremaud's book, and the goal is clearly attained. The presentation is clear, concise and self-contained, all the necessary concepts are put on a firm ground and proofs are worked out in great detail...In summary, the interested reader will find in Bremaud's book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier and wavelet basics."