Discrete and Continuous Wavelet Expansions

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Discrete and Continuous Wavelet Expansions. / Dem'Yanovich, Yuri; Bich, Le Thi Nhu.

в: WSEAS Transactions on Mathematics, Том 21, 23.02.2022, стр. 58-67.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

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Dem'Yanovich, Yuri ; Bich, Le Thi Nhu. / Discrete and Continuous Wavelet Expansions. в: WSEAS Transactions on Mathematics. 2022 ; Том 21. стр. 58-67.

BibTeX

@article{546f69d07d1d4517aa8784d46f78b5e6,

title = "Discrete and Continuous Wavelet Expansions",

abstract = "This paper proposes a new approach to the construction of wavelet decomposition, which is suitable for processing a wide range of information flows. The proposed approach is based on abstract functions with values in linear topological spaces. It is defined by embedded spaces and their projections. The proposed approach allows for adaptive ways of decomposition for the initial flow depending on the speed changes of the last one. The initial information flows can be real number flows, flows of complex and p-adic numbers, as well as flows of (finite or infinite) vectors, matrices, etc. The result is illustrated with examples of spline-wavelet decompositions of discrete flows, and also with the example of the decomposition of a continuous flow.",

keywords = "calibration relations, decomposition, flows, reconstruction, wavelets",

author = "Yuri Dem'Yanovich and Bich, {Le Thi Nhu}",

year = "2022",

month = feb,

day = "23",

doi = "10.37394/23206.2022.21.9",

language = "English",

volume = "21",

pages = "58--67",

journal = "WSEAS Transactions on Mathematics",

issn = "1109-2769",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - Discrete and Continuous Wavelet Expansions

AU - Dem'Yanovich, Yuri

AU - Bich, Le Thi Nhu

PY - 2022/2/23

Y1 - 2022/2/23

N2 - This paper proposes a new approach to the construction of wavelet decomposition, which is suitable for processing a wide range of information flows. The proposed approach is based on abstract functions with values in linear topological spaces. It is defined by embedded spaces and their projections. The proposed approach allows for adaptive ways of decomposition for the initial flow depending on the speed changes of the last one. The initial information flows can be real number flows, flows of complex and p-adic numbers, as well as flows of (finite or infinite) vectors, matrices, etc. The result is illustrated with examples of spline-wavelet decompositions of discrete flows, and also with the example of the decomposition of a continuous flow.

AB - This paper proposes a new approach to the construction of wavelet decomposition, which is suitable for processing a wide range of information flows. The proposed approach is based on abstract functions with values in linear topological spaces. It is defined by embedded spaces and their projections. The proposed approach allows for adaptive ways of decomposition for the initial flow depending on the speed changes of the last one. The initial information flows can be real number flows, flows of complex and p-adic numbers, as well as flows of (finite or infinite) vectors, matrices, etc. The result is illustrated with examples of spline-wavelet decompositions of discrete flows, and also with the example of the decomposition of a continuous flow.

KW - calibration relations

KW - decomposition

KW - flows

KW - reconstruction

KW - wavelets

UR - http://www.scopus.com/inward/record.url?scp=85126598095&partnerID=8YFLogxK

U2 - 10.37394/23206.2022.21.9

DO - 10.37394/23206.2022.21.9

M3 - Article

AN - SCOPUS:85126598095

VL - 21

SP - 58

EP - 67

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -

ID: 97349467

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