An Introduction to Wavelets
- 1st Edition, Volume 1 - January 3, 1992
- Imprint: Academic Press
- Editor: Charles K. Chui
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 1 7 4 5 8 4 - 4
- Paperback ISBN:9 7 8 - 1 - 4 9 3 3 - 0 0 2 7 - 3
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 4 9 9 0 6 - 2
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 emphas… Read more
Purchase options
Institutional subscription on ScienceDirect
Request a sales quoteAn 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.
- 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
Academics and researchers, research and development engineers in industry, and graduate-level students
An Overview: From Fourier Analysis to Wavelet Analysis. The Integral Wavelet Transform and Time-Frequency Analysis. Inversion Formulas and Duals. Classification of Wavelets. Multiresolution Analysis, Splines, and Wavelets. Wavelet Decompositions and Reconstructions. Fourier Analysis: Fourier and Inverse Fourier Transforms. Continuous-Time Convolution and the Delta Function. Fourier Transform of Square-Integrable Functions. Fourier Series. Basic Convergence Theory and Poisson's Summation Formula. Wavelet Transforms and Time-Frequency Analysis: The Gabor Transform. Short-Time Fourier Transforms and the Uncertainty Principle. The Integral Wavelet Transform. Dyadic Wavelets and Inversions. Frames. Wavelet Series. Cardinal Spline Analysis: Cardinal Spline Spaces. B-Splines and Their Basic Properties. The Two-Scale Relation and an Interpolatory Graphical Display Algorithm. B-Net Representations and Computation of Cardinal Splines. Construction of Spline Approximation Formulas. Construction of Spline Interpolation Formulas. Scaling Functions and Wavelets: Multiresolution Analysis. Scaling Functions with Finite Two-Scale Relations. Direct-Sum Decompositions of L2(R). Wavelets and Their Duals. Linear-Phase Filtering. Compactly Supported Wavelets. Cardinal Spline-Wavelets: Interpolaratory Spline-Wavelets. Compactly Supported Spline-Wavelets. Computation of Cardinal Spline-Wavelets. Euler-Frobenius Polynomials. Error Analysis in Spline-Wavelet Decomposition. Total Positivity, Complete Oscillation, Zero-Crossings. Orthogonal Wavelets and Wavelet Packets: Examples of Orthogonal Wavelets. Identification of Orthogonal Two-Scale Symbols. Construction of Compactly Supported Orthogonal Wavelets. Orthogonal Wavelet Packets. Orthogonal Decomposition of Wavelet Series. Notes. References. Subject Index. Appendix.
- Edition: 1
- Volume: 1
- Published: January 3, 1992
- No. of pages (Hardback): 266
- Imprint: Academic Press
- Language: English
- Hardback ISBN: 9780121745844
- Paperback ISBN: 9781493300273
- eBook ISBN: 9780080499062
Read An Introduction to Wavelets on ScienceDirect