Geodesic
Periodic interpolating-orthogonal bases of MRA and wavelets
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1467-1474

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The paper is devoted to the construction of interpolating-orthogonal periodic bases of mutiresolution analysis and corresponding wavelets from the existing orthogonal bases of wavelets. The mask $m(\omega)$ of an orthogonal scaling function $\varphi(x)$ is converted in such a way that the new scaling function $\varphi^I (x)$ generates an interpolation and orthogonal system of integer shifts. According to the resulting system, periodic bases of scaling functions and wavelets are constructed.
Keywords: wavelet, scaling function, multiresolution analysis, interpolating wavelet, orthogonal wavelet, periodic wavelet. 
@article{SEMR_2021_18_2_a73,
     author = {E. A. Pleshcheva},
     title = {Periodic interpolating-orthogonal bases of {MRA} and wavelets},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1467--1474},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a73/}
}
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E. A. Pleshcheva. Periodic interpolating-orthogonal bases of MRA and wavelets. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1467-1474. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a73/