Введение в вэйвлеты: Для студентов вузов по специальности ''Прикладная математика''

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.

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. 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