05b_4-Clickers-Fourier Transforms

05b_4-Clickers-Fourier Transforms - 2-1Fourier...

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Unformatted text preview: 2-1Fourier Transforms2-2Fourier TransformsFourier Seriesf(t)=g(ϖ)eiϖt-∞∞∫f(t)=cnen=-∞∞∑i nϖt2-3Fourier TransformsFourier Seriesf(t)=g(ϖ)eiϖt-∞∞∫d(what?)f(t)=cnen=-∞∞∑i nϖtA)dxB)dtC)dωD)Nothing is needed, just E)Something else/not suref(t)=g(ϖ)eiϖt∞∫2-4Fourier TransformsFourier Seriesf(t)=g(ϖ)eiϖt-∞∞∫dϖf(t)=cnen=-∞∞∑i nϖtcn=1Tf(t)e-i nϖtT∫dtg(ϖ)∝f(t)eiwhat?dwhat?-∞∞∫A) f(t)e-inϖtdt-∞∞∫B) f(t)e-iϖtdt-∞∞∫C) f(t)e-i nϖtdϖ-∞∞∫D) f(t)e-iϖtdϖ-∞∞∫E) Something else/not sure?2-5Fourier TransformsFourier Seriesf(t)=g(ϖ)eiϖt-∞∞∫dϖf(t)=cnen=-∞∞∑i nϖtcn=1Tf(t)e-i nϖtT∫dtg(ϖ)=12πf(t)e-iϖtdt-∞∞∫2-6If f(t) is periodic (period T), then we can write it as a Fourier series:What is the formula for cn? f(t)=cnen=-∞∞∑i nϖtA) f(t)e-i nϖtT∫dϖB) f(t)e-i nϖtT∫dtC) 1ϖf(t)e-i nϖtT∫dϖD) 1Tf(t)e-i nϖtT∫dtE) Something else/not sure?2-7limit, as T∞Fourier Series (period T)...
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05b_4-Clickers-Fourier Transforms - 2-1Fourier...

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