Rationally related frequencies and the Fourier Series representation Suppose that we have the signal $$x(t) = e^{j\omega t} + e^{j\frac{3}{2} \omega t},$$ and we want to find a Fourier Series representation for that signal. Is this possible? According to my understanding, since the ratio of the frequencies of the two complex exponentials above is a rational number, the signal is periodic. Since it is periodic, it is possible to represent the signal as $$x(t) = \sum_{k = -\infty}^{\infty} a_k e^{jk\omega_0t},$$
where $\omega_0$ is the fundamental frequency of the signal?
Yes, that's easily possible. The fundamental frequency of the given signal is $\omega_0=\omega/2$, and its Fourier series coefficients are

$$a_k=\begin{cases}1,\quad k\in\{2,3\}\\0,\quad\text{otherwise}\end{cases}$$