Adaptive Wavelet-Analysis
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Adaptive Wavelet-Analysis: Theorie und Software

Adaptive Wavelet-Analysis: Theorie und Software


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About the Book

Dieses Buch richtet sich an angewandte Mathematiker, Ingenieure und Naturwissenschaftler, die Computerprogramme zur Wavelet-Analysis (und hierzu verwandter Methoden) in der Signalverarbeitung reeller Daten entwickeln und einsetzen. Dem weniger an Anwendungen interessierten Leser dient das Buch als Einfuhrung in einige wesentliche Aspekte der Wavelet-Theorie; der akademische Lehrer kann es als Textbuch mit einer Darstellung aktuellster mathematischer Techniken in der transienten Signalanalysis einsetzen.Nach einem einfuhrenden Kapitel, das die erforderlichen mathematischen Hilfsmittel darstellt, behandelt der Autor die Eigenschaften von Wellenformen, die in der adaptiven Wavelet-Analysis Anwendung finden: Diskrete schnelle Fourier-Transformationen, orthogonale Funktionen mit uberlappendem Trager. Weitere Kapitel diskutieren die Methode der "besten Basis", die Zeit-Frequenz-Analyse und Kombinationen dieser Algorithmen, die fur die Analyse und Verarbeitung von Signalen, Rauschunterdruckung und Datenkompression nutzlich sind.Jedes Kapitel geht auf die technischen Aspekte der Implementierung der behandelten Algorithmen ein, indem Beispiele von Pseudocodes eingestreut sind.

Table of Contents:
1 Mathematische Vorbetrachtungen.- 1.1 Grundlagen aus der Analysis.- 1.2 Funktionenräume.- 1.3 Fourier-Analysis.- 1.4 Approximation.- 1.5 Übungsaufgaben.- 2 Programmiertechniken.- 2.1 Rechnen unter realen Bedingungen.- 2.2 Strukturen.- 2.3 Verknüpfungen.- 2.4 Übungsaufgaben.- 3 Diskrete Fourier-Transformation.- 3.1 Die Fourier-Transformation auf CN.- 3.2 Die diskrete Hartley-Transformation.- 3.3 Diskrete Sinus- und Cosinus-Transformationen.- 3.4 Übungsaufgaben.- 4 Lokale trigonometrische Transformationen.- 4.1 Hilfsmittel und Beispiele.- 4.2 Orthogonalbasen.- 4.3 Implementierung der Grundoperationen.- 4.4 Implementierung adaptiver Transformationen.- 4.5 Übungsaufgaben.- 5 Quadraturfilter.- 5.1 Definitionen und grundlegende Eigenschaften.- 5.2 Phasenantwort.- 5.3 Frequenzantwort.- 5.4 Implementierung der Faltungs-Dezimation.- 5.5 Übungsaufgaben.- 6 Diskrete Wavelet-Transformation.- 6.1 Einige Grundtatsachen über Wavelets.- 6.2 Implementierungen.- 6.3 Übungsaufgaben.- 7 Wavelet-Pakete.- 7.1 Definitionen und allgemeine Eigenschaften.- 7.2 Implementierungen.- 7.3 Übungsaufgaben.- 8 Der Algorithmus der besten Basis.- 8.1 Definitionen.- 8.2 Bestimmung der besten Basis.- 8.3 Implementierung.- 8.4 Übungsaufgaben.- 9 Mehrdimensionale Bibliotheksbäume.- 9.1 Mehrdimensionale Zerlegungsoperatoren.- 9.2 Praktische Überlegungen.- 9.3 Implementierungen.- 9.4 Übungsaufgaben.- 10 Zeit-Frequenz-Analyse.- 10.1 Die Zeit-Frequenz-Ebene.- 10.2 Zeit-Frequenz-Analyse einiger wichtiger Signale.- 10.3 Implementierung.- 10.4 Übungsaufgaben.- 11 Einige Anwendungen.- 11.1 Bildkompression.- 11.2 Schnelle genäherte Faktoranalyse.- 11.3 Matrixmultiplikation in Nichtstandard-Form.- 11.4 Segmentierung von Sprachsignalen.- 11.5 Sprachwirrwarr.- 11.6 Adaptive Rauschunterdrückung durchWellenformen.- A Lösungen für einige Übungsaufgaben.- B Symbolliste.- C Koeffizienten der Quadraturfilter.- C.1 Orthogonale Quadraturfilter.- C.1.1 Beylkin-Filter.- C.1.2 Coifman- oder „Coiflet“-Filter.- C.1.3 Standard-Daubechies-Filter.- C.1.4 Vaidyanathan-Filter.- C.2 Biorthogonale Quadraturfilter.- C.2.1 Symmetrisch/antisymmetrisch, ein Moment.- C.2.2 Symmetrisch/symmetrisch, zwei Momente.- C.2.3 Symmetrisch/antisymmetrisch, drei Momente.- Sachwortverzeichnis.

About the Author :
Professor Dr. Mladen Victor Wickerhauser lehrt an der University in St. Louis, Missouri, USA.


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Product Details
  • ISBN-13: 9783322831286
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Vieweg+Teubner Verlag
  • Height: 240 mm
  • No of Pages: 440
  • Sub Title: Theorie und Software
  • ISBN-10: 3322831280
  • Publisher Date: 05 Jan 2012
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Width: 170 mm


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