Propagation of Random Errors by the Discrete Wavelet Transform Algorithm

Propagation of Random Errors by the Discrete Wavelet Transform Algorithm

The paper presents considerations concerning the transfer of random errors from the input to the output of the Discrete Wavelet Transform (DWT) algorithm. The concept of determining an uncertainty of its output data based on the probabilistic error description has been presented. The DWT is discusse...

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Bibliographic Details
Main Authors: Jerzy Roj, Łukasz Dróżdż
Format: Article
Language:English
Published: MDPI AG 2021-03-01
Series:Electronics
Subjects:
digital signal processing
wavelet transform
error propagation
uncertainty
algorithm coefficients identification
Online Access:https://www.mdpi.com/2079-9292/10/7/764
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spelling doaj-cffb402aeef34fb5a39d5634ce36220c2021-03-25T00:01:58ZengMDPI AGElectronics2079-92922021-03-011076476410.3390/electronics10070764Propagation of Random Errors by the Discrete Wavelet Transform AlgorithmJerzy Roj0Łukasz Dróżdż1Department of Measurement Science, Electronics and Control, Silesian University of Technology, 44-100 Gliwice, PolandDepartment of Measurement Science, Electronics and Control, Silesian University of Technology, 44-100 Gliwice, PolandThe paper presents considerations concerning the transfer of random errors from the input to the output of the Discrete Wavelet Transform (DWT) algorithm. The concept of determining an uncertainty of its output data based on the probabilistic error description has been presented. The DWT is discussed as the product of the vector of input quantities and the matrix of algorithm coefficients. Calculations of the uncertainty of a single output result of the algorithm are described with assumption that the input quantities are burdened by random errors of known distributions. Theoretical considerations have been verified by simulation experiments using the Monte Carlo method. Determining the uncertainty at the DWT output is possible due to the specific properties of transferring random errors by linear and additive algorithms.https://www.mdpi.com/2079-9292/10/7/764digital signal processingwavelet transformerror propagationuncertaintyalgorithm coefficients identification
collection DOAJ
language English
format Article
sources DOAJ
author Jerzy Roj
Łukasz Dróżdż
spellingShingle Jerzy Roj
Łukasz Dróżdż
Propagation of Random Errors by the Discrete Wavelet Transform Algorithm
Electronics
digital signal processing
wavelet transform
error propagation
uncertainty
algorithm coefficients identification
author_facet Jerzy Roj
Łukasz Dróżdż
author_sort Jerzy Roj
title Propagation of Random Errors by the Discrete Wavelet Transform Algorithm
title_short Propagation of Random Errors by the Discrete Wavelet Transform Algorithm
title_full Propagation of Random Errors by the Discrete Wavelet Transform Algorithm
title_fullStr Propagation of Random Errors by the Discrete Wavelet Transform Algorithm
title_full_unstemmed Propagation of Random Errors by the Discrete Wavelet Transform Algorithm
title_sort propagation of random errors by the discrete wavelet transform algorithm
publisher MDPI AG
series Electronics
issn 2079-9292
publishDate 2021-03-01
description The paper presents considerations concerning the transfer of random errors from the input to the output of the Discrete Wavelet Transform (DWT) algorithm. The concept of determining an uncertainty of its output data based on the probabilistic error description has been presented. The DWT is discussed as the product of the vector of input quantities and the matrix of algorithm coefficients. Calculations of the uncertainty of a single output result of the algorithm are described with assumption that the input quantities are burdened by random errors of known distributions. Theoretical considerations have been verified by simulation experiments using the Monte Carlo method. Determining the uncertainty at the DWT output is possible due to the specific properties of transferring random errors by linear and additive algorithms.
topic digital signal processing
wavelet transform
error propagation
uncertainty
algorithm coefficients identification
url https://www.mdpi.com/2079-9292/10/7/764
work_keys_str_mv AT jerzyroj propagationofrandomerrorsbythediscretewavelettransformalgorithm
AT łukaszdrozdz propagationofrandomerrorsbythediscretewavelettransformalgorithm
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