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Determine whether the functions given can be represented by a Fourier series, a) $x(t)=\cos 6 t+\sin 8 t+e^{i 2 t}$ b) $x(t)=\cos (t)+\sin \Pi t$
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written 3.0 years ago by
prajapatijaimin
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Solution:
(a) $x(t)=\cos 6 t+\sin 8 t+e^{i 2 t}$
$ \begin{aligned}\\ & T_1=\frac{2 \Pi}{6}=\frac{\Pi}{3} \quad T_2=\frac{2 \Pi}{8}=\frac{\Pi}{4} \quad T_3=2 \Pi / 2=\Pi \\\\ & \frac{T_1}{T_2}=\frac{\pi / 3}{\Pi / 4}=\frac{4}{3} \quad \frac{T_1}{T_3}=\frac{\Pi / 3}{\Pi}=\frac{1}{3}\\ \end{aligned} $
Rational numbers, so periodic, so it can be represented by Fourier series.
$ \begin{gathered} \text …
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