An Introduction to Wavelets (Volume 1) (Wavelet Analysis and Its Applications, Volume 1)

An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field. Key Features • This is an introductory treatise on wavelet analysis, with an emphasis on spline-wavelets and time-frequency analysis • This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis • Suitable as a textbook for a beginning course on wavelet analysis Audience: Academics and researchers, research and development engineers in industry, and graduate-level students. Content: Wavelet Analysis and Its Applications Page ii Front Matter Page iii Copyright page Page iv Dedication Page v Preface Pages ix-x Charles K. Chui 1 - An Overview Pages 1-22 2 - Fourier Analysis Pages 23-48 3 - Wavelet Transforms and Time-Frequency Analysis Pages 49-80 4 - Cardinal Spline Analysis Pages 81-117 5 - Scaling Functions and Wavelets Pages 119-176 6 - Cardinal Spline-Wavelets Pages 177-214 7 - Orthogonal Wavelets and Wavelet Packets Pages 215-243 Notes Pages 245-249 References Pages 251-255 Subject Index Pages 257,259-264 Part of "Wavelet Analysis And Its Applications" series, this book presents an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. It covers such topics as: time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and more. Wavelets are considered by many to be the most powerful mathematical tool for signal and image processing. This CD-ROM boxed set contains three items: a copy of the text "An Introduction to Wavelets", a CD containing wavelets and signal processing software, and a booklet that serves as the manual for the software. Examines the Integral Wavelet Transform (IWT), which has the property of zooming in on short-lived, high-frequency phenomena. It covers Fourier transforms, time and frequency localization, discrete-time analysis, spline analysis, multi-resolution analysis and B- and orthogonal wavelets