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Ten Lectures on Wavelets
Abstract
Introduction Preliminaries and notation The what, why, and how of wavelets The continuous wavelet transform Discrete wavelet transforms: Frames Time-frequency density and orthonormal bases Orthonormal bases of wavelets and multiresolutional analysis Orthonormal bases of compactly supported wavelets More about the regularity of compactly supported wavelets Symmetry for compactly supported wavelet bases Characterization of functional spaces by means of wavelets Generalizations and tricks for orthonormal wavelet bases References Indexes.
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“However, the phase functions of the orthogonal wavelet and scaling filters, which are used in DWT and MODWT, are not linear [49].”
From Translation-Invariant Zero-Phase Wavelet Methods for Feature Extraction in Terahertz Time-Domain Spectroscopy (2022) · cites this paper as [49]
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Adami, M., Rudorff, B. F. T., de Freitas, R. M., Aguiar, D. A., Sugawara, L. M., & Mello, M. P. (2012) · Sustainability · doi:10.3390/su4040574 · Cited by 208
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Metadata
- Authors
- Daubechies, I.
- Affiliations
- Rutgers, The State University of New Jersey (US)
- Corresponding author
- Daubechies, Ingrid
- ORCID
- Daubechies, Ingrid
- Venue
- Computers in Physics
- Published
- 1992-01-01
- Volume
- 6
- Issue
- 6
- Pages
- 697-697
- ISSN
- 0894-1866 (ISSN-L)
- OpenAlex
- W2062024414
- Cited by
- 15,979
- References
- 0
- Citations by year
- 2026: 132 · 2025: 91 · 2024: 72 · 2023: 93 · 2022: 95 · 2021: 300 · 2020: 347 · 2019: 346 · 2018: 376 · 2017: 381 · 2016: 462 · 2015: 613 · 2014: 611 · 2013: 664 · 2012: 701
- FWCI
- 239.79
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Computers in Physics (publishedVersion)
- Society for Industrial and Applied Mathematics eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Keywords
- wavelets, continuous wavelet transform, discrete wavelet transform, wavelet frames, orthonormal bases, multiresolution analysis, compactly supported wavelets, wavelet regularity, time-frequency analysis
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