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Title: Discrete wavelet transform - Wikipedia

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(Top) https://en.wikipedia.org/wiki/Discrete_wavelet_transform
1 Definition https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Definition
1.1 One level of the transform https://en.wikipedia.org/wiki/Discrete_wavelet_transform#One_level_of_the_transform
1.2 Cascading and filter banks https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Cascading_and_filter_banks
1.3 Relationship to the mother wavelet https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Relationship_to_the_mother_wavelet
1.4 Time complexity https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Time_complexity
2 Examples https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Examples
2.1 Haar wavelets https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Haar_wavelets
2.2 Daubechies wavelets https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Daubechies_wavelets
2.3 The dual-tree complex wavelet transform (DCWT) https://en.wikipedia.org/wiki/Discrete_wavelet_transform#The_dual-tree_complex_wavelet_transform_(DCWT)
2.4 Others https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Others
2.5 Coding https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Coding
3 Properties https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Properties
3.1 Time issues https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Time_issues
4 Applications https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Applications
4.1 Image processing https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Image_processing
4.2 Watermarking https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Watermarking
5 Similar transforms https://en.wikipedia.org/wiki/Discrete_wavelet_transform#Similar_transforms
6 See also https://en.wikipedia.org/wiki/Discrete_wavelet_transform#See_also
7 References https://en.wikipedia.org/wiki/Discrete_wavelet_transform#References
8 External links https://en.wikipedia.org/wiki/Discrete_wavelet_transform#External_links
Catalàhttps://ca.wikipedia.org/wiki/Transformada_discreta_d%27ondeta
Češtinahttps://cs.wikipedia.org/wiki/Diskr%C3%A9tn%C3%AD_vlnkov%C3%A1_transformace
Deutschhttps://de.wikipedia.org/wiki/Wavelet-Transformation#Diskrete_Wavelet-Transformation
فارسیhttps://fa.wikipedia.org/wiki/%D8%AA%D8%A8%D8%AF%DB%8C%D9%84_%D9%85%D9%88%D8%AC%DA%A9_%DA%AF%D8%B3%D8%B3%D8%AA%D9%87
Françaishttps://fr.wikipedia.org/wiki/Ondelette#Transformée_en_ondelettes_discrète
日本語https://ja.wikipedia.org/wiki/%E9%9B%A2%E6%95%A3%E3%82%A6%E3%82%A7%E3%83%BC%E3%83%96%E3%83%AC%E3%83%83%E3%83%88%E5%A4%89%E6%8F%9B
한국어https://ko.wikipedia.org/wiki/%EC%9D%B4%EC%82%B0_%EC%9B%A8%EC%9D%B4%EB%B8%94%EB%A6%BF_%EB%B3%80%ED%99%98
Portuguêshttps://pt.wikipedia.org/wiki/Transformada_discreta_de_wavelet
Русскийhttps://ru.wikipedia.org/wiki/%D0%94%D0%B8%D1%81%D0%BA%D1%80%D0%B5%D1%82%D0%BD%D0%BE%D0%B5_%D0%B2%D0%B5%D0%B9%D0%B2%D0%BB%D0%B5%D1%82-%D0%BF%D1%80%D0%B5%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5
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JPEG2000https://en.wikipedia.org/wiki/JPEG2000
clarification neededhttps://en.wikipedia.org/wiki/Wikipedia:Please_clarify
numerical analysishttps://en.wikipedia.org/wiki/Numerical_analysis
functional analysishttps://en.wikipedia.org/wiki/Functional_analysis
wavelet transformhttps://en.wikipedia.org/wiki/Wavelet_transform
waveletshttps://en.wikipedia.org/wiki/Wavelet
Fourier transformshttps://en.wikipedia.org/wiki/Fourier_transform
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low-pass filterhttps://en.wikipedia.org/wiki/Low-pass_filter
impulse responsehttps://en.wikipedia.org/wiki/Impulse_response
convolutionhttps://en.wikipedia.org/wiki/Convolution
high-pass filterhttps://en.wikipedia.org/wiki/High-pass_filter
quadrature mirror filterhttps://en.wikipedia.org/wiki/Quadrature_mirror_filter
https://en.wikipedia.org/wiki/File:Wavelets_-_DWT.png
subsampledhttps://en.wikipedia.org/wiki/Downsampling
subsampling operatorhttps://en.wikipedia.org/wiki/Downsampling
Lifting schemehttps://en.wikipedia.org/wiki/Lifting_scheme
edithttps://en.wikipedia.org/w/index.php?title=Discrete_wavelet_transform&action=edit§ion=3
binary treehttps://en.wikipedia.org/wiki/Binary_tree
filter bankhttps://en.wikipedia.org/wiki/Filter_bank
https://en.wikipedia.org/wiki/File:Wavelets_-_Filter_Bank.png
https://en.wikipedia.org/wiki/File:Wavelets_-_DWT_Freq.png
edithttps://en.wikipedia.org/w/index.php?title=Discrete_wavelet_transform&action=edit§ion=4
discrete set of child waveletshttps://en.wikipedia.org/wiki/Wavelet#Discrete_wavelet_transforms_.28discrete_shift_and_scale_parameters.29
scale parameterhttps://en.wikipedia.org/wiki/Scale_parameter
convolutionhttps://en.wikipedia.org/wiki/Convolution
Haar wavelethttps://en.wikipedia.org/wiki/Haar_wavelet
edithttps://en.wikipedia.org/w/index.php?title=Discrete_wavelet_transform&action=edit§ion=5
O(N)https://en.wikipedia.org/wiki/Big_O_notation
fast Fourier transformhttps://en.wikipedia.org/wiki/Fast_Fourier_transform
O(N)https://en.wikipedia.org/wiki/Big_O_notation
O(N)https://en.wikipedia.org/wiki/Big_O_notation
recurrence relationhttps://en.wikipedia.org/wiki/Recurrence_relation
O(N)https://en.wikipedia.org/wiki/Big_O_notation
geometric serieshttps://en.wikipedia.org/wiki/Geometric_series
Haar wavelethttps://en.wikipedia.org/wiki/Haar_wavelet
[1]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-Barina2020-1
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Haar wavelethttps://en.wikipedia.org/wiki/Haar_wavelet
Alfréd Haarhttps://en.wikipedia.org/wiki/Alfr%C3%A9d_Haar
Haar wavelethttps://en.wikipedia.org/wiki/Haar_wavelet
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Daubechies wavelethttps://en.wikipedia.org/wiki/Daubechies_wavelet
Ingrid Daubechieshttps://en.wikipedia.org/wiki/Ingrid_Daubechies
recurrence relationshttps://en.wikipedia.org/wiki/Recurrence_relation
waveletshttps://en.wikipedia.org/wiki/Daubechies_wavelet
[2]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-2
[3]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-3
[4]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-4
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Complex wavelet transformhttps://en.wikipedia.org/wiki/Complex_wavelet_transform
[5]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-5
edithttps://en.wikipedia.org/w/index.php?title=Discrete_wavelet_transform&action=edit§ion=10
JPEG 2000https://en.wikipedia.org/wiki/JPEG_2000
JPEG XShttps://en.wikipedia.org/wiki/JPEG_XS
[6]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-6
[7]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-7
[8]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-8
Binomial QMFhttps://en.wikipedia.org/wiki/Binomial_QMF
Ali Naci Akansuhttps://en.wikipedia.org/wiki/Ali_Naci_Akansu
[9]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-9
set partitioning in hierarchical treeshttps://en.wikipedia.org/wiki/Set_partitioning_in_hierarchical_trees
[10]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-Said-10
non- or undecimated wavelet transformhttps://en.wikipedia.org/wiki/Stationary_wavelet_transform
Newland transformhttps://en.wikipedia.org/wiki/Newland_transform
orthonormalhttps://en.wikipedia.org/wiki/Orthonormal
top-hat filtershttps://en.wikipedia.org/wiki/Top-hat_filter
frequency spacehttps://en.wikipedia.org/wiki/Frequency_space
Wavelet packet transformshttps://en.wikipedia.org/wiki/Wavelet_packet_decomposition
Complex wavelet transformhttps://en.wikipedia.org/wiki/Complex_wavelet_transform
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Haarhttps://en.wikipedia.org/wiki/Haar_wavelet
Daubechieshttps://en.wikipedia.org/wiki/Daubechies_wavelet
Coiflethttps://en.wikipedia.org/wiki/Coiflet
Legendrehttps://en.wikipedia.org/wiki/Legendre_wavelet
JWavehttps://github.com/cscheiblich/JWave
CDFhttps://en.wikipedia.org/wiki/Cohen-Daubechies-Feauveau_wavelet
Chttps://en.wikipedia.org/wiki/C_(programming_language)
JPEG 2000https://en.wikipedia.org/wiki/JPEG_2000
image compressionhttps://en.wikipedia.org/wiki/Image_compression
herehttps://web.archive.org/web/20120305164605/http://www.embl.de/~gpau/misc/dwt97.c
Haar wavelethttps://en.wikipedia.org/wiki/Haar_wavelet
Javahttps://en.wikipedia.org/wiki/Java_(programming_language)
https://en.wikipedia.org/wiki/File:Haar_DWT_of_the_Sound_Waveform_%22I_Love_Wavelets%22.png
time domainhttps://en.wikipedia.org/wiki/Time_domain
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Fast wavelet transformhttps://en.wikipedia.org/wiki/Fast_wavelet_transform
fast Fourier transformhttps://en.wikipedia.org/wiki/Fast_Fourier_transform
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[11]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-11
[12]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-12
[13]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-13
edithttps://en.wikipedia.org/w/index.php?title=Discrete_wavelet_transform&action=edit§ion=14
signal codinghttps://en.wikipedia.org/w/index.php?title=Signal_coding&action=edit&redlink=1
data compressionhttps://en.wikipedia.org/wiki/Data_compression
[14]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-14
[15]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-15
[16]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-16
[17]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-17
[18]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-18
[19]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-19
[20]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-20
ultra-widebandhttps://en.wikipedia.org/wiki/Ultra-wideband
[21]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-21
edithttps://en.wikipedia.org/w/index.php?title=Discrete_wavelet_transform&action=edit§ion=15
https://en.wikipedia.org/wiki/File:Noise_Wavelet.jpg
https://en.wikipedia.org/wiki/File:Denosied_Wavelet.jpg
Gaussian noisehttps://en.wikipedia.org/wiki/Gaussian_noise
Matlabhttps://en.wikipedia.org/wiki/Matlab
biorthogonalhttps://en.wikipedia.org/wiki/Biorthogonal_wavelet
[22]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-22
wavelet transformationhttps://en.wikipedia.org/wiki/Wavelet_transform
[23]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-23
signal-to-noise-ratiohttps://en.wikipedia.org/wiki/Signal-to-noise_ratio
citation neededhttps://en.wikipedia.org/wiki/Wikipedia:Citation_needed
[24]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-24
discrete Fourier transformhttps://en.wikipedia.org/wiki/Discrete_Fourier_transform
unit impulsehttps://en.wikipedia.org/wiki/Unit_impulse
DFT matrixhttps://en.wikipedia.org/wiki/DFT_matrix
orthogonalhttps://en.wikipedia.org/wiki/Orthogonal
orthonormalhttps://en.wikipedia.org/wiki/Orthonormal
https://en.wikipedia.org/wiki/File:Sinc_function_(normalized).svg
sinc functionhttps://en.wikipedia.org/wiki/Sinc_function
undershoothttps://en.wikipedia.org/wiki/Undershoot_(signal)
ringinghttps://en.wikipedia.org/wiki/Ringing_(signal)
low-pass filteredhttps://en.wikipedia.org/wiki/Low-pass_filter
undershoothttps://en.wikipedia.org/wiki/Undershoot_(signal)
ringinghttps://en.wikipedia.org/wiki/Ringing_(signal)
edithttps://en.wikipedia.org/w/index.php?title=Discrete_wavelet_transform&action=edit§ion=16
Watermarkinghttps://en.wikipedia.org/wiki/Digital_watermarking
DCThttps://en.wikipedia.org/wiki/Discrete_cosine_transform
[25]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-25
https://en.wikipedia.org/wiki/File:5-level_discrete_wavelet_transform.png
imperceptibilityhttps://en.wikipedia.org/wiki/Digital_watermarking#Perceptibility
robustnesshttps://en.wikipedia.org/wiki/Digital_watermarking#Robustness
Laplacian of Gaussian (LoG)https://en.wikipedia.org/wiki/Blob_detection#The_Laplacian_of_Gaussian
edithttps://en.wikipedia.org/w/index.php?title=Discrete_wavelet_transform&action=edit§ion=17
Adam7 algorithmhttps://en.wikipedia.org/wiki/Adam7_algorithm
interlacinghttps://en.wikipedia.org/wiki/Interlacing_(bitmaps)
Portable Network Graphicshttps://en.wikipedia.org/wiki/Portable_Network_Graphics
Haar waveletshttps://en.wikipedia.org/wiki/Haar_wavelet
downsampleshttps://en.wikipedia.org/wiki/Downsample
decimatinghttps://en.wikipedia.org/wiki/Decimation_(signal_processing)
low-pass filteringhttps://en.wikipedia.org/wiki/Low-pass_filter
pixelationhttps://en.wikipedia.org/wiki/Pixelation
[26]https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_note-atto16tgrs-26
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Discrete cosine transformhttps://en.wikipedia.org/wiki/Discrete_cosine_transform
Wavelethttps://en.wikipedia.org/wiki/Wavelet
Wavelet transformhttps://en.wikipedia.org/wiki/Wavelet_transform
Wavelet compressionhttps://en.wikipedia.org/wiki/Wavelet_compression
List of wavelet-related transformshttps://en.wikipedia.org/wiki/List_of_wavelet-related_transforms
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^https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_ref-Barina2020_1-0
"Real-time wavelet transform for infinite image strips"https://rdcu.be/b5vdo
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10.1007/s11554-020-00995-8https://doi.org/10.1007%2Fs11554-020-00995-8
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220396648https://api.semanticscholar.org/CorpusID:220396648
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Perfect Reconstruction Binomial QMF-Wavelet Transformhttp://web.njit.edu/~akansu/PAPERS/Akansu-BinomialQMF-Wavelet-SPIE-VCIP-Sept1990.pdf
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978-0-12-047141-6https://en.wikipedia.org/wiki/Special:BookSources/978-0-12-047141-6
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Filter Banks and Wavelets in Signal Processing: A Critical Reviewhttps://web.njit.edu/~akansu/PAPERS/Akansu-FilterBanksWaveletsSP-SPIEOct1993.pdf
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^https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_ref-6
"General characteristics and design considerations for temporal subband video coding"https://www.itu.int/wftp3/av-arch/video-site/0312_Wai/VCEG-U06.doc
ITU-Thttps://en.wikipedia.org/wiki/ITU-T
Video Coding Experts Grouphttps://en.wikipedia.org/wiki/Video_Coding_Experts_Group
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The Essential Guide to Video Processinghttps://books.google.com/books?id=wXmSPPB_c_0C&pg=PA355
Academic Presshttps://en.wikipedia.org/wiki/Academic_Press
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9780080922508https://en.wikipedia.org/wiki/Special:BookSources/9780080922508
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10.1109/ICASSP.1988.196696https://doi.org/10.1109%2FICASSP.1988.196696
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Ali Naci Akansuhttps://en.wikipedia.org/wiki/Ali_Naci_Akansu
An Efficient QMF-Wavelet Structurehttp://web.njit.edu/~akansu/NJITSYMP1990/AkansuNJIT1STWAVELETSSYMPAPRIL301990.pdf
^https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_ref-Said_10-0
"A new, fast, and efficient image codec based on set partitioning in hierarchical trees"https://www.researchgate.net/publication/2835826
doihttps://en.wikipedia.org/wiki/Doi_(identifier)
10.1109/76.499834https://doi.org/10.1109%2F76.499834
ISSNhttps://en.wikipedia.org/wiki/ISSN_(identifier)
1051-8215https://search.worldcat.org/issn/1051-8215
^https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_ref-11
^https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_ref-12
^https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_ref-13
^https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_ref-14
"Novel method for stride length estimation with body area network accelerometers"https://www.youtube.com/watch?v=DTpEVQSEBBk
^https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_ref-15
Bibcodehttps://en.wikipedia.org/wiki/Bibcode_(identifier)
2019IRAL....4.3449Nhttps://ui.adsabs.harvard.edu/abs/2019IRAL....4.3449N
doihttps://en.wikipedia.org/wiki/Doi_(identifier)
10.1109/LRA.2019.2926666https://doi.org/10.1109%2FLRA.2019.2926666
ISSNhttps://en.wikipedia.org/wiki/ISSN_(identifier)
2377-3766https://search.worldcat.org/issn/2377-3766
S2CIDhttps://en.wikipedia.org/wiki/S2CID_(identifier)
198474004https://api.semanticscholar.org/CorpusID:198474004
^https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_ref-16
"Wavelet Based Methods in Image Processing"http://www.rose-hulman.edu/~brought/Epubs/Imaging/waveimage.html
^https://en.wikipedia.org/wiki/Discrete_wavelet_transform#cite_ref-17
"Quantization Noise of Multilevel Discrete Wavelet Transform Filters in Image Processing"https://doi.org/10.3103/S8756699018060092
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Orthogonal Transmultiplexers in Communication: A Reviewhttp://web.njit.edu/~akansu/PAPERS/AKANSU-ORTHOGONAL-MUX-1998.pdf
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Wavelet Transforms in Signal Processing: A Review of Emerging Applicationshttp://web.njit.edu/~akansu/PAPERS/ANA-IWS-WAS-ELSEVIER%20PHYSCOM%202010.pdf
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"Thresholds for wavelet 1-D using Birgé-Massart strategy - MATLAB wdcbm"https://www.mathworks.com/help/wavelet/ref/wdcbm.html
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"how to get SNR for 2 images - MATLAB Answers - MATLAB Central"https://www.mathworks.com/matlabcentral/answers/71609-how-to-get-snr-for-2-images
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https://link.springer.com/chapter/10.1007%2F978-3-642-25327-0_28https://link.springer.com/chapter/10.1007%2F978-3-642-25327-0_28
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"Wavelet Operators and Multiplicative Observation Models—Application to SAR Image Time-Series Analysis"https://hal.archives-ouvertes.fr/hal-01341064/file/TGRS-2015-00943_GeomWavelets%5B18%5D_Final%20-%20VersionHAL.pdf
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