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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2020.tde-17092020-140359
Document
Author
Full name
Deyvid Toledo Santiago de Almeida
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Chiann, Chang (President)
Montoril, Michel Helcias
Sáfadi, Thelma
Title in Portuguese
Análise de variância utilizando ondaletas
Keywords in Portuguese
Análise de Fourier
Análise de ondaletas
Análise de variância em séries temporais
Abstract in Portuguese
Análise de Variância no contexto de séries temporais possui a inconveniência da presença de correlação entre as observações. Nessa dissertação, foram estudados métodos de análise de sinais, mais precisamente análise de Fourier e análise de ondaletas (Wavelets), que são ferramentas capazes de transformar o sinal original em uma nova entidade matemática descorrelacionada que possui domínio diferente do original, possibilitando a aplicação da análise de variância sem violar a hipótese de independência dessa metodologia. A diferença mais relevante entre as técnicas é que a análise de Fourier é própria para sinais estacionários, enquanto a análise de ondaletas é robusta a sinais não estacionários pelo fato de sua transformada possuir aspecto local. Na comparação dos resultados por meio de dados simulados, ambas as técnicas convergiram para um mesmo resultado. Para aplicação em dados, reais foram utilizadas medidas de Pico de Fluxo Expiratório (PFE) ao longo do tempo de crianças e adolescentes com condição asmática, ou não, e expostas ao fumo domiciliar, ou não. Na aplicação da ANOVA dois fatores, ambas as metodologias convergiram no teste de interação, mas ocorreram algumas divergências nos testes dos fatores isoladamente.
Title in English
Analysis of variance using wavelets
Keywords in English
Analysis of variance in time series
Fourier analysis
Wavelet analysis
Abstract in English
Analysis of Variance in time series context has a correlation problem between observations. In this dissertation, signal analysis methods were studied, more exactly Fourier analysis and wavelet Analysis, which are tools that transform the original signal into a new mathematical entity that has distinct domain from the original, allowing the application of analysis of variance without violating the independence hypothesis of this tool. The most relevant difference between the techniques is that the Fourier analysis is suitable for stationary signals while the wavelet Analysis is robust to non-stationary signals, because its transform has a local aspect. When comparing the results in simulated data, both techniques converged to the same results. For application in real data, measures were taken over the time of Peak Expiratory Flow (PEF) of children and adolescents with or without asthma and exposed or not to smoking environment in their homes. In two-way ANOVA aplication, both techniques converged by the interaction test, but there were some divergent results by factor tests separately.
 
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Publishing Date
2021-02-04
 
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