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Everything about Wavelet
Function for integral Fourier-like transform
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: WaveletA 5-minute orientation
- Skim a recent paper: A Review of Wavelet Analysis and Its Applications: Challenges and OpportunitiesInfluential work since 2022
- Pick up a classic book: Discrete Fourier Analysis and WaveletsThe most-reprinted book on the subject
- Read the landmark paper: A theory for multiresolution signal decomposition: the wavelet representationCited 17,052 times
- Go sideways: Wavelet transformA closely related topic
- Go sideways: Daubechies waveletA closely related topic
📖 Definitions
Noun A small wave; a ripple.
Noun A fast-decaying oscillation.
🏆 Landmark papers (most cited)
A theory for multiresolution signal decomposition: the wavelet representation
A Practical Guide to Wavelet Analysis
Ideal spatial adaptation by wavelet shrinkage
Application of the cross wavelet transform and wavelet coherence to geophysical time series
The wavelet transform, time-frequency localization and signal analysis
Embedded image coding using zerotrees of wavelet coefficients
Adapting to Unknown Smoothness via Wavelet Shrinkage
WAVELET TRANSFORMS AND THEIR APPLICATIONS TO TURBULENCE
🆕 Influential since 2022
A Review of Wavelet Analysis and Its Applications: Challenges and Opportunities
Haar wavelet downsampling: A simple but effective downsampling module for semantic segmentation
Multi-stage image denoising with the wavelet transform
Underwater Image Enhancement via Weighted Wavelet Visual Perception Fusion
Wavelet transform for rotary machine fault diagnosis:10 years revisited
📚 Books worth reading
- 📕Discrete Fourier Analysis and WaveletsS. Allen Broughton, Kurt Bryan · 2011
The illustrated wavelet transform handbookPaul S. Addison · 2002
Discrete Wavelet TransformationsPatrick J. Van Fleet · 2011
Wavelets and multiwaveletsFritz Keinert · 2003
Primer on Wavelets and Their Scientific ApplicationsJames S. Walker · 2008- 📕Two-Dimensional Wavelets and Their RelativesJean-Pierre Antoine, Romain Murenzi · 2004
- 📕Compressed sensingYonina C. Eldar · 2012
- 📕Statistical Modeling by WaveletsBrani Vidakovic · 2008
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Wavelet transform In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated…
- Daubechies wavelet The Daubechies wavelets, based on the work of Ingrid Daubechies, are a family of orthogonal wavelets defining a discrete wavelet transform and characterized…
- Discrete wavelet transform In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled…
- Multiresolution analysis A multiresolution analysis (MRA) or multiscale approximation (MSA) is the design method of most of the practically relevant discrete wavelet transforms…
- Haar wavelet In mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is…
- Wavelet packet decomposition Originally known as optimal subband tree structuring (SB-TS), also called wavelet packet decomposition (WPD; sometimes known as just wavelet packets or…
- Vanishing moment Vanishing moments are a fundamental concept in wavelet theory, signal processing, and functional analysis. They describe a property of a wavelet or function…
- Constant-Q transform In mathematics and signal processing, the constant-Q transform and variable-Q transform, simply known as CQT and VQT, transforms a data series to the frequency…