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Wavelets generated by the Rudin-Shapiro polynomials

100%
Abdollahi A., Cheshmavar J., Taghavi M.
Open Mathematics
|
2011
|
tom 9
|
nr 2
441-448
EN
In this paper, we consider the well-known Rudin-Shapiro polynomials as a class of constant multiples of low-pass filters to construct a sequence of compactly supported wavelets.
2
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Closure of dilates of shift-invariant subspaces

76%
Soto-Bajo M.
Open Mathematics
|
2013
|
tom 11
|
nr 10
1785-1799
EN
Let V be any shift-invariant subspace of square summable functions. We prove that if for some A expansive dilation V is A-refinable, then the completeness property is equivalent to several conditions on the local behaviour at the origin of the spectral function of V, among them the origin is a point of A*-approximate continuity of the spectral function if we assume this value to be one. We present our results also in a more general setting of A-reducing spaces. We also prove that the origin is a point of A*-approximate continuity of the Fourier transform of any semiorthogonal tight frame wavelet if we assume this value to be zero.
3
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A general construction of nonseparable multivariate orthonormal wavelet bases

76%
Karoui A.
Open Mathematics
|
2008
|
tom 6
|
nr 4
504-525
EN
The construction of nonseparable and compactly supported orthonormal wavelet bases of L 2(R n); n ≥ 2, is still a challenging and an open research problem. In this paper, we provide a special method for the construction of such wavelet bases. The wavelets constructed by this method are dyadic wavelets. Also, we show that our proposed method can be adapted for an eventual construction of multidimensional orthogonal multiwavelet matrix masks, candidates for generating multidimensional multiwavelet bases.
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