A First Course in Wavelets with Fourier Analysis (Hardcover)

Albert Boggess, Francis J. Narcowich

  • 出版商: Prentice Hall
  • 出版日期: 2009-09-01
  • 定價: $1,250
  • 售價: 9.5$1,188
  • 語言: 英文
  • 頁數: 336
  • 裝訂: Hardcover
  • ISBN: 0470431172
  • ISBN-13: 9780470431177
  • 立即出貨 (庫存=1)

買這商品的人也買了...

商品描述

A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition

Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level.

The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature:

  • The development of a Fourier series, Fourier transform, and discrete Fourier analysis

  • Improved sections devoted to continuous wavelets and two-dimensional wavelets

  • The analysis of Haar, Shannon, and linear spline wavelets

  • The general theory of multi-resolution analysis

  • Updated MATLAB code and expanded applications to signal processing

  • The construction, smoothness, and computation of Daubechies' wavelets

  • Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform

Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples.

A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.

商品描述(中文翻譯)

《傅立葉分析與小波的全面、自成體系的教材──現已推出新版》

透過廣泛的內容和易於理解的解釋,《傅立葉分析與小波的初級課程,第二版》提供了一個自成體系的數學教材,涵蓋了傅立葉分析和小波的基本概念,同時獨特地呈現了信號分析的應用和問題。為了使本書適合廣大讀者,作者將基本概念和基礎思想以易於理解的方式呈現,並將其應用於信號處理的初級水平。

本書以向量空間、內積空間和其他分析的初步主題作為開端。隨後的章節包括:
- 傅立葉級數、傅立葉變換和離散傅立葉分析的發展
- 關於連續小波和二維小波的改進部分
- Haar、Shannon和線性樣條小波的分析
- 多分辨率分析的一般理論
- 更新的MATLAB代碼和擴展的信號處理應用
- Daubechies小波的構造、平滑度和計算
- 高維小波、分解和重構以及小波變換等高級主題

本書提供了信號處理的應用,其中大多數涉及音頻或視頻信號的過濾和壓縮。其中一些應用首先在傅立葉分析的背景下介紹,然後在小波的章節中進一步探討。新的練習題引入了額外的應用,每個理論的討論都附有完整的證明。廣泛的附錄提供了更高級的證明和練習的部分解答,以及更新的MATLAB例程,補充了所呈現的示例。

《傅立葉分析與小波的初級課程,第二版》是一本適合高年級本科生和研究生的數學和工程課程的優秀教材。對於希望在初級水平上學習小波理論和傅立葉分析的數學家、信號處理工程師和科學家來說,它也是一個寶貴的資源。