TY - JOUR

T1 - Continuum Wavelets and Distributions

AU - Dem'Yanovich, Yuri K.

AU - Ivantsova, Olga N.

AU - Ponomareva, Aleksandra Y.

N1 - Publisher Copyright: © 2022 World Scientific and Engineering Academy and Society. All rights reserved.

PY - 2022/7/14

Y1 - 2022/7/14

N2 - The purpose of this work is to obtain a wavelet expansion of information flows, which are distribution flows (in the terminology of Schwartz). The concept of completeness is introduced for a family of abstract functions. Using the mentioned families, nested spaces of distribution flows are constructed. The projection of the enclosing space onto the nested space generates a wavelet expansion. Decomposition and reconstruction formulas for the above expansion are derived. These formulas can be used for wavelet expansion of the original information flow coming from the analog device. This approach is preferable to the approach in which the analog flow is converted into a discrete numerical flow using quantization and digitization. The fact is that quantization and digitization lead to significant loss of information and distortion. This paper also considers the wavelet expansion of a discrete flow of distributions using the Haar type functions.

AB - The purpose of this work is to obtain a wavelet expansion of information flows, which are distribution flows (in the terminology of Schwartz). The concept of completeness is introduced for a family of abstract functions. Using the mentioned families, nested spaces of distribution flows are constructed. The projection of the enclosing space onto the nested space generates a wavelet expansion. Decomposition and reconstruction formulas for the above expansion are derived. These formulas can be used for wavelet expansion of the original information flow coming from the analog device. This approach is preferable to the approach in which the analog flow is converted into a discrete numerical flow using quantization and digitization. The fact is that quantization and digitization lead to significant loss of information and distortion. This paper also considers the wavelet expansion of a discrete flow of distributions using the Haar type functions.

KW - calibration relations

KW - distributions

KW - information flows

KW - wavelets

UR - http://www.scopus.com/inward/record.url?scp=85139732904&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/0ee9173d-cc84-390a-a4a7-ed8332520a3f/

U2 - 10.37394/23206.2022.21.62

DO - 10.37394/23206.2022.21.62

M3 - Article

AN - SCOPUS:85139732904

VL - 21

SP - 553

EP - 562

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -