An introduction to wavelets through linear algebra / Michael W. Frazier

Auteur: Frazier, Michael (1956-) - AuteurType de document: Monographie Collection: Undergraduate texts in mathematics Langue: anglaisPays: Etats UnisÉditeur: New York : Springer, 1999Description: 1 vol. (XVI-501 p.) : fig. ; 25 cm ISBN: 9780387986395 ; rel. Résumé: The mathematical theory of wavelets is less than 15 years old, yet already wavelets have become a fundamental tool in many areas of applied mathematics and engineering. This introduction to wavelets assumes a basic background in linear algebra (reviewed in Chapter 1) and real analysis at the undergraduate level. Fourier and wavelet analyses are first presented in the finite-dimensional context, using only linear algebra. Then Fourier series are introduced in order to develop wavelets in the infinite-dimensional, but discrete context. Finally, the text discusses Fourier transform and wavelet theory on the real line. The computation of the wavelet transform via filter banks is emphasized, and applications to signal compression and numerical differential equations are given. This text is ideal for a topics course for mathematics majors, because it exhibits and emerging mathematical theory with many applications. It also allows engineering students without graduate mathematics prerequisites to gain a practical knowledge of wavelets. (Source : 4ème de couverture).Bibliographie: Bibliogr. p. 484-490. Index. Sujets MSC: 42C40 Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems
42-01 Harmonic analysis on Euclidean spaces -- Instructional exposition (textbooks, tutorial papers, etc.)
00A06 General -- General and miscellaneous specific topics -- Mathematics for nonmathematicians (engineering, social sciences, etc.)
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Bibliogr. p. 484-490. Index

The mathematical theory of wavelets is less than 15 years old, yet already wavelets have become a fundamental tool in many areas of applied mathematics and engineering. This introduction to wavelets assumes a basic background in linear algebra (reviewed in Chapter 1) and real analysis at the undergraduate level. Fourier and wavelet analyses are first presented in the finite-dimensional context, using only linear algebra. Then Fourier series are introduced in order to develop wavelets in the infinite-dimensional, but discrete context. Finally, the text discusses Fourier transform and wavelet theory on the real line. The computation of the wavelet transform via filter banks is emphasized, and applications to signal compression and numerical differential equations are given. This text is ideal for a topics course for mathematics majors, because it exhibits and emerging mathematical theory with many applications. It also allows engineering students without graduate mathematics prerequisites to gain a practical knowledge of wavelets. (Source : 4ème de couverture)

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