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I want to obtain the energy of this signal $$x_i(t)= e^{j2\pi(2i-1)f_0t}$$ where $f_0 = 1$ Hz, $i= 1,...,4$ and $j$ is a complex. I think I need to use the Fourier transform or the Parseval theorem but I'm not sure how to apply it.

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  • $\begingroup$ You can just take the squared magnitude and integrate it between to time bounds, and see what happen $\endgroup$ May 7, 2021 at 17:57

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As mentioned in the comments you can just take the integral of the squared magnitude.

Notice that the magnitude of $|e^{a+bj}| = |e^a||e^{bj}| = e^a$ for $a,b \in \mathbb{R}$, comparing with your function we see that $|x_i(t)|=1$. We conclude that $x_i(t)$ is a power signal, not an energy signal, i.e. you must define a time interval to integrate. Then the energy will be $\int_{t_0}^{t_f} |x_i(t)|^2 \mathrm{d}t = (t_f - t_0)$. I hope this helps.

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  • $\begingroup$ Cleanly done. I just correcting the upright $\mathrm{d}$ $\endgroup$ May 7, 2021 at 18:38

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