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:* <math>S^m(t)</math> is [[orthogonal]] to <math>P^{(m)}(A_0)</math>, that is, <math>\int_R S^m(t)\, f(t)\, dt=0 ==Strömberg wavelets of order 0== ...

...by this wavelet is minimized. However they have the downside of being non-orthogonal, so efficient decomposition into the basis is difficult. Since their incept |title=Image Representation Using 2D Gabor wavelets ...

{{Short description|Types of wavelets}} ...l another context, the terminology is used to describe a family of complex wavelets indexed by positive integers which are connected with the derivatives of th ...

...nal to be a [[Sparse matrix|sparse]] presentation, which is the reason why wavelets can be applied for [[image compression]].<ref>{{cite thesis | title = Coiflet-type wavelets: Theory, design, and applications ...

The '''Meyer wavelet''' is an orthogonal [[wavelet]] proposed by [[Yves Meyer]].<ref>{{cite book |last1=Meyer |first *{{cite book|last1=Daubechies|first1=Ingrid|title=Ten Lectures on Wavelets (CBMS-NSF conference series in applied mathematics)|date=September 1992|pub ...

...h>\int_{\mathbb{R}}\psi(t)dt=0</math>. Consequently, continuous fractional wavelets must oscillate and behave as bandpass filters in the fractional Fourier dom ...t3 = N.-T. | year = 2015 | title = Multiresolution analysis and orthogonal wavelets associated with fractional wavelet transform | journal = Signal, Image, Vid ...

...if|thumb|right|Animation showing the compactly supported cardinal B-spline wavelets of orders 1, 2, 3, 4 and 5.]] ...name=Daubechies>{{cite book|last1=Ingrid Daubechies|title=Ten Lectures on Wavelets|url=https://archive.org/details/tenlecturesonwav0000daub|url-access=registr ...

...n |first=A. |title=Decomposition of Hardy functions into square integrable wavelets of constant shape |journal=SIAM Journal on Mathematical Analysis |volume=15 ...has vanishing moments up to order <math>n</math> if it is [[Orthogonality|orthogonal]] to all polynomials of degree <math>n-1</math> or lower. ...

</math> is an orthogonal basis for <math>V_N ...completely spread out spectrum and have the perfectly incoherent with Haar wavelets. ...

...the whole basis. Therefore, we must use large amounts of Fourier basis or Wavelets to represent whole signal with small approximation error. Some [[matching p Since <math>\varphi_{t_0,f_0,\sigma}(t)\quad</math> are not orthogonal,<math>\quad a_{t_0,f_0,\sigma}\quad</math> should be determined by a [[matc ...

..._i}</math> denotes the [[Projection (linear algebra)#Orthogonal projection|orthogonal projection]] onto the subspace <math>W_i</math>. The constants <math>A</mat ...za|first1=P.G.|last2=Kutyniok|author2-link=Gitta Kutyniok|first2=G. |title=Wavelets, Frames and Operator Theory |chapter=Frames of subspaces |date=2004|volume= ...

* Form [[orthogonal basis]] in the value function space ...idhar; Maggioni, Mauro. (2005) Value function approximation with diffusion wavelets and Laplacian eigenfuctions. Proceedings of Advances in Neural Information ...

...e flexible space-frequency signal decomposition several filters (including wavelets) have been proposed. The Log-Gabor<ref name="field">D. J. Field. [https://w ...cas.cz/files/Soutez_08/Publikace/gabor_07.pdf Self-invertible 2D log-Gabor wavelets]. Int. Journal of Computational Vision, 2007</ref> These detected edges can ...

...ing digital data on multiple [[Carrier wave|carrier]] frequencies with non-orthogonal intervals between frequency of sub-carriers.<ref name=patent>RU2054684 (C1) ...r spacing <math>\alpha/T</math> for <math>\alpha < 1</math> makes them non-orthogonal over each symbol period. ...

...or spectral-band-concentrated while space- or time-limited) that form an [[orthogonal basis]] for bandlimited or spacelimited spaces. They are widely used as bas I. Daubechies. ''Ten Lectures on Wavelets''. SIAM, 1992, {{isbn|0-89871-274-2}} ...

...d analysis bank.<ref>{{Cite book|title = Multidimensional filter banks and Wavelets, Basic theory and cosine modulated filter banks|author1 = Sankar Basu|autho ...1117/12.618209|chapter = Multidimensional oversampled filter banks|title = Wavelets XI|series=Proceedings of SPIE |volume = 5914|pages = 591424|year = 2005|las ...

...rix]], its eigenvectors <math>\{\mu_l\}_{l=0,\cdots, N-1}</math> form an [[orthogonal basis]]. Hence an inverse graph Fourier transform (IGFT) exists, and it is ...dergheynst|first2=Pierre|last3=Gribonval|first3=Rémi|date=2011-03-01|title=Wavelets on graphs via spectral graph theory|url=http://www.sciencedirect.com/scienc ...

...onary''. Atoms in the dictionary are not required to be [[Orthogonal basis|orthogonal]], and they may be an over-complete spanning set. This problem setup also a ...al component analysis]] which require atoms <math>d_1,...,d_n</math> to be orthogonal. The choice of these subspaces is crucial for efficient dimensionality re ...

...interval (0,&nbsp;1). Although the correlation can be reduced by using [[orthogonal polynomials]], it is generally more informative to consider the fitted regr ...

...er operator is just the Dirac operator. In representation theory for the [[orthogonal group]], O(''n'') it is common to consider functions taking values in space ...st=Mitrea | first=M. | title=Singular Integrals, Hardy Spaces and Clifford Wavelets |series=Lecture Notes in Mathematics |volume=1575 |publisher=[[Springer Ver ...