Title
A First Course on Wavelets (Studies in Advanced Mathematics),New
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Wavelet theory had its origin in quantum field theory, signal analysis, and function space theory. In these areas waveletlike algorithms replace the classical Fouriertype expansion of a function. This unique new book is an excellent introduction to the basic properties of wavelets, from background math to powerful applications. The authors provide elementary methods for constructing wavelets, and illustrate several new classes of wavelets.The text begins with a description of local sine and cosine bases that have been shown to be very effective in applications. Very little mathematical background is needed to follow this material. A complete treatment of bandlimited wavelets follows. These are characterized by some elementary equations, allowing the authors to introduce many new wavelets. Next, the idea of multiresolution analysis (MRA) is developed, and the authors include simplified presentations of previous studies, particularly for compactly supported wavelets.Some of the topics treated include: Several bases generated by a single function via translations and dilationsMultiresolution analysis, compactly supported wavelets, and spline waveletsBandlimited waveletsUnconditionality of wavelet basesCharacterizations of many of the principal objects in the theory of wavelets, such as lowpass filters and scaling functionsThe authors also present the basic philosophy that all orthonormal wavelets are completely characterized by two simple equations, and that most properties and constructions of wavelets can be developed using these two equations. Material related to applications is provided, and constructions of splines wavelets are presented.Mathematicians, engineers, physicists, and anyone with a mathematical background will find this to be an important text for furthering their studies on wavelets.
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This product may contain chemicals known to the State of California to cause cancer, birth defects, or other reproductive harm.
For more information, please visit www.P65Warnings.ca.gov.
- Q: What is the page count of the book? A: The book contains five hundred twelve pages. This length allows for a comprehensive exploration of wavelet theory.
- Q: What are the dimensions of the book? A: The book measures nine point twenty-one inches in length, six point fourteen inches in width, and nine point seventy-two inches in height. These dimensions make it a suitable size for both reading and reference.
- Q: What type of binding does the book have? A: The book is bound in hardcover. This sturdy binding enhances durability and longevity for readers.
- Q: How do I apply the concepts from the book? A: You can apply the concepts by studying the methods for constructing wavelets presented in the text. The book includes practical applications that illustrate the use of wavelets in various fields.
- Q: Is this book suitable for beginners? A: Yes, this book is suitable for beginners with a basic mathematical background. It provides elementary methods and explanations that are easy to follow.
- Q: What level of mathematics is required to understand this book? A: Very little mathematical background is needed to follow the material. The authors present concepts in an accessible manner for readers new to wavelet theory.
- Q: How should I care for this book? A: To keep the book in good condition, store it in a dry place away from direct sunlight. Avoid bending the pages to preserve the spine.
- Q: Is this book safe for children? A: Yes, the book's content is academically focused and suitable for older children interested in mathematics. However, adult supervision may be beneficial for younger readers.
- Q: What is the publisher of this book? A: The book is published by CRC Press. This reputable publisher is known for its high-quality academic and professional texts.
- Q: What topics are covered in the book? A: The book covers topics such as multiresolution analysis, band-limited wavelets, and the characterization of wavelet bases. Each subject is treated in detail to enhance understanding.
- Q: How can I use this book for further studies? A: You can use this book as a foundational text for advanced studies in wavelet theory. It provides essential knowledge that is applicable to various fields, including engineering and physics.
- Q: Are there examples included in the book? A: Yes, the book includes examples that illustrate the construction and application of different wavelet classes. These examples help solidify the concepts presented.
- Q: What audience is this book intended for? A: The book is intended for mathematicians, engineers, physicists, and anyone with a mathematical background. It serves as an important resource for a diverse array of professionals.
- Q: What is the main focus of the book? A: The main focus of the book is to provide an introduction to wavelet theory and its applications. It aims to explain the basic properties and methods of wavelet construction.
- Q: Can I find advanced topics in this book? A: Yes, the book includes advanced topics such as unconditionality of wavelet bases and characterizations of wavelet theory. This makes it suitable for both beginners and advanced readers.