Análise de Fourier e Transformadas - Exercícios Resolvidos

gt 2 2 cos 2t π sen 3t π2π w0 1 2 2 e d 2t π e j 2t π e j 3t e j 3t 2j Σ ak e jwokt k 2 e jπ e j 2t e j π e j 2t 1 2j e j 3t 1 2j e j 3t Σ ak e jwokt k 2 to 2 k to a0 a2 a2 a3 a3 logo a0 2 a2 e d π cos π j sen π 1 a3 1 2j 1 2j 2j 2j 2j 4j 2 2j 4 1 2 j a2 e j π cos π j sen π 1 a3 1 2j 1 2j 2j 2j 2j 4j 2 2j 4 1 2 j ak 0 k 0 2 e 3 logo ak 2 k 0 1 k 2 e k 2 1 2 j k 3 1 2 j k 3 0 k 0 2 e 3 ak 2 k 0 1 k 2 e k 2 1 2 k 3 e k 3 0 k 0 2 e 3 φk 0 k 0 π ou π k 2 e k 2 π 2 k 3 3π 2 ou π 2 k 3 0 k 0 2 e 3 Bogo ak 4 3 2 1 0 1 2 3 4 kw0 12 φk 4 3 2 1 0 1 2 3 4 kw0 Sinal ímpar pois f t f t logo a0 bk 0 T 4 w0 2π T 2π 4 π 2 rads Ck 2 T T ft sen w0 kt dt 4 T 0 T2 ft sen π 2 kt dt Ck 4 4 01 2 t sen π 2 kt dt 21 sen π 2 kt dt Ck 02 sen π 2 kt dt 01 t sen π 2 kt dt 21 sen π 2 kt dt Ck 2 π 2 k cos π 2 kt 0 1 t π 2 cos π 2 kt 1 π k 2 sen π 2 kt 0 1 cos π 2 kt π k 2 1 2 Ck 2 π 2 cos π 2 k 1 1 π 2 cos π 2 k 1 π k 2 sen π 2 k cos π k cos π 2 k π k 2 Ck 2 π 2 cos π 2 k 2 π 2 1 π 2 cos π 2 k 1 π k 2 sen π 2 k 1 π 2 cos π k 1 π 2 cos π 2 k Ck 1 π k 2 2 cos π k 1 π k 2 sen π 2 k Ck 2 π k 2 1 k 2 π k sen π 2 k Ck 2 π k 2 1 k 2 π k sen π 2 k se k ímpar 2 π k 2 1 k se k par yt x1te3jt x2t2 Yjω X1jω3 X2jω ej2ω F F yt F x1t e3jt x2t2 Y jω F x1t e3jt F x2t2 Y jω X1jω3 X2jω ej2ω X1jω F egt ut egt ut ejωt dt egjωt dt X1jω 19jω e9jωt 0 19jω 0 1 19jω X2jω F e2t ut2 e2t ut2 ejωt dt X2jω 2 to e2jωt dt 12jω e2jωt 2 X2jω 12jω 0 e2jω 2 12jω e 42jω logo Y jω X1jω3 X2jω ej2ω Y jω 19jω3 12jω e 4 2jω ej2ω Y jω e4 9jω3 2jω Fim