Example of Computation of Fourier series of a CT SIGNAL

A practice problem on "Signals and Systems"

Fourier series coefficients for CT signal

CT Signal

$ \, x(t)=6sin(6t) $

Fourier series coefficients

$ x(t)=\sum_{k=-\infty}^\infty a_k e^{jk\omega_0 t} $

$ \, x(t)=6sin(6t) = 6\cdot\frac{e^{j6t}-e^{-j6t}}{2j}=\frac{3(e^{j6t}-e^{-j6t})}{j} $

$ \, x(t)=\frac{3e^{j6t}}{j}-\frac{3e^{-j6t}}{j} $

$ \, a_1 = \frac{3}{j}\ ,\ a_{-1} = \frac{-3}{j} $

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