Wavelet and Fourier Analysis Basics

Author: Albert Boggess Francis J. Narcowich
Publisher:
Publish Date: 2004-01-01
Features: The book has very distinct features: It is a book that undergraduate or graduate students in engineering can understand. The translator, starting from their work, has been teaching the "Wavelet Transform and Its Applications" course to graduate students in communication and information systems since 1998. They have reviewed more than ten candidate domestic and international textbooks, all of which shared the same problem: these wavelet books were too mathematical. They required knowledge of measure theory and other advanced topics, which general engineering students did not possess, leading to a fear of learning. At the same time, wavelet theory has achieved fruitful results in many engineering fields, compelling a large number of engineering technicians to be eager to try it. The author has long been engaged in teaching Fourier analysis and wavelet theory, and their rich experience and achievements are fully demonstrated in this book. It is rare to encounter such a book. The main purpose of this book is to show readers many basic knowledge of Fourier analysis and wavelets, as well as their applications in signal analysis. The book is divided into 8 chapters and 2 appendices. The preface is the prerequisite for learning Chapters 1 to 7, which is the inner product space. Chapter 1 explains the basic knowledge of Fourier series. Chapter 2 explains the Fourier transform. Chapter 3 introduces the discrete Fourier transform and the fast Fourier transform. Chapters 4 to 7 discuss wavelets, with a focus on the construction of orthogonal wavelets. The appendices introduce more complex technical topics and provide MATLAB code for demonstrating concepts or generating graphics. The application fields of wavelet analysis are very broad, including: many disciplines in the digital field: signal analysis, image processing; quantum mechanics, theoretical physics; military electronic countermeasures and intelligent weapons; computer classification and recognition; artificial synthesis of music and language; medical imaging and diagnosis; geological exploration data processing; fault diagnosis of large machinery, and other aspects. Many articles and reference books on wavelets require readers to have a complex mathematical background, but this book only requires students to have a good understanding of calculus and linear algebra. It is easy to understand and serves as a basic textbook for senior undergraduate and graduate students in mathematics, computer science, electronics, communication, geology, medicine, and mechanical engineering. It can also be used as a reference book for related technical personnel.