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* * * SÉRIE DE FOURIER UNIVERSIDADE FEDERAL DE PERNAMBUCO CENTRO DE TECNOLOGIA E GEOCIÊNCAS Departamento de Engenharia Elétrica e Sistemas de Potência * * * Série de Fourier Função Periódica Função Repete em intervalos constantes To Período To Menor intervalo de repetição To=2 s Onda triangular To=1 s Meia onda * * * Série de Fourier Função Periódica Gerada com o conhecimento de um período * * * Série de Fourier Conceitos Básicos Fontes Funções periódicas aproximadamente senoidais Elementos não-linear Formas de onda não-senoidais * * * Série de Fourier Conceitos Básicos Componente com freqüência nula (Contínua) + Componente com freqüência igual função (Fundamental) + Componentes com freqüência múltiplas da fundamental (Harmônicas) * * * Série de Fourier Conceitos Básicos * * * Série de Fourier Conceitos Básicos * * * Série de Fourier Exemplo f(t) é periódica * * * Série de Fourier Exemplo * * * Série de Fourier Exemplo * * * Série de Fourier Exemplo f(t) não é periódica * * * Série de Fourier Exemplo * * * Série de Fourier Problema f(t) é periódica ? Determine To , wo e wn * * * Série de Fourier Coeficientes de Fourier Relação dos parâmetros * * * Série de Fourier Coeficientes de Fourier * * * Série de Fourier Coeficientes de Fourier * * * Série de Fourier Coeficientes de Fourier * * * Série de Fourier Coeficientes de Fourier * * * Série de Fourier Exemplo * * * Série de Fourier Exemplo f(t) simétrica com eixo t Valor médio nulo * * * Série de Fourier Exemplo f(t) simétrica com eixo ordenadas * * * Série de Fourier Exemplo * * * Série de Fourier Exemplo * * * Série de Fourier Exemplo COEFICIENTES * * * Série de Fourier Exemplo * * * Série de Fourier Condições de Existência Condição fraca de DIRICHLET * * * Série de Fourier Condições de Convergência Descontinuidades Valor médio de f(t) * * * Série de Fourier Condições de Convergência * * * Série de Fourier Condições de Convergência Gráf1 -0.0381913677 -1 -0.0254630337 -1 -0.0127321535 -1 0 1 0.0127321535 1 0.0254630337 1 0.0381913677 1 0.0509158826 1 0.0636353059 1 0.0763483658 1 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