A first course in wavelets with Fourier analysis

This book presents many of the essential ideas behind Fourier analysis and wavelets along with some of their applications to signal analysis. The applications to signal processing are kept elementary, without much use of the technical jargon of the subject, in an effort for the material to be accessible to a wide audience. The preliminary topics dealing with vector spaces, inner productspaces, and other topics in analysis are presented in Chapter 0. Fourier series, Fourier transform, and Discrete Fourier analysis are presented in Chapters1, 2, and 3. Wavelets are introduced in Chapter 4 with the simplest case: Haar wavelets. Chapters 5 presents the general theory of multi-resolution analysis after the reader has seen the ideas presented in the case of Haar wavelets. The celebrated Daubechies compactly supported wavelets are presented in Chapter 6 and further topics are presented in Chapter 7. Applications to signal processing are provided throughout the text. Most of these applications involve the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and then reappear in the chapters on wavelets with comparisons on how the two techniques perform. Further applications are presented in the exercises. Proofs of most of the theory are contained in the text, and some of the more complicated proofs are placed in the Appendix.

• ISBN: 978-0-470-43117-7
• Editorial: John Wiley & Sons
• Encuadernacion: Cartoné
• Páginas: 336
• Fecha Publicación: 04/09/2009
• Nº Volúmenes: 1
• Idioma: Inglés