1. (10 pts.) Using duality between Fourier series and DTFT, determine the complex Fourier series coefficients of the following periodic signals: $s(t) = frac{15}{17 - 8 cos(2pi t)}$ $x(t) = egin{cases} 1 - |t|, & 0 le |t| le 1 \ 0, & 1 < |t| le 2 end{cases}$ $(T_0 = 4)$
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Using the duality property, we can write: S(f) = 15 Ī“(f) + 17Ļ [Ī“(f-27) + Ī“(f+27)] - 4j [e^(-j2Ļf) + e^(j2Ļf)] ā«(1 to 2) e^(-j2Ļft) dt where Ī“(f) is the Dirac delta function and Ī“(f-a) is the shifted delta function. Show moreā¦
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