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An Introduction to Wavelets
Abstract
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.
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Cited by
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Metadata
- Authors
- Chui, C. K., & Heil, C.
- Venue
- Computers in Physics
- Publisher
- AIP Publishing
- Published
- 1992-11-01
- Volume
- 6
- Issue
- 6
- Pages
- 697-697
- ISSN
- 0894-1866 (ISSN-L)
- OpenAlex
- W1489213177
- Cited by
- 4,732
- References
- 0
- FWCI
- 161.80
- Type
- journal article
- Language
- en
- Open access
- closed
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