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I saw a piece of code on github which transforms the planetary movement into the fourier wave function.

These circles are given by the x and y ordinates: x=cos(ωt) y=sin(ωt), which are periodic. Usually, we can apply it to get the frequency components - spectrum of the signal as @Brendan Darrer suggest. Which is a very useful concept, when talking about electromagnetic signal for example. However, when we step further and have a closer look about the intersection the plot below gives us, what can we interpret from these intersection points.

To help us see this question more clearly, we can imagine it as a star system just like our solar system. As we can see visually in the plot below, there are four wave functions in the plot. Though they have the different frequency (rotation period), they will intersect at specific time. At the intersection of two wave functions,say, 4sin(3θ)/3pi and 4sin(5θ)/5pi, it suggests that these two planets will have the same phase at their orbit and have the same projected displacement (same y value) mathematically. My question is, what would happen when two wave functions intersect in a Fourier series representation of periodic signals?

Any thoughts would be greatly appreciated.

enter image description here

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    $\begingroup$ What do you mean by intersection? $\endgroup$
    – ProfRob
    Jul 27, 2022 at 10:07
  • $\begingroup$ I am referring to the intersections we can see visually in the plot above. There are four wave functions in the plot and they have the different frequency. They will intersect at specific time. But that's just the mathematical meaning, and I want to know what the physical meaning of this intersection is? @ProfRob $\endgroup$
    – Kevin
    Jul 27, 2022 at 10:18
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    $\begingroup$ didn’t you ask a nearly identical question yesterday? $\endgroup$ Jul 27, 2022 at 10:47
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    $\begingroup$ I've deleted my answer. Can you explain how two planets can have the same projected displacement at the same value of $\theta$, if $\theta \neq 0$? $\endgroup$
    – ProfRob
    Jul 27, 2022 at 13:22
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    $\begingroup$ @Kevin in such cases better to edit the old question… $\endgroup$ Jul 27, 2022 at 13:59

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These circles are given by the $x$ and $y$ ordinates: $x = cos(\omega t)$ $y = sin(\omega t)$, which are periodic. If talking about anything, electromagnetic signal, acoustic pressure etc, one can apply a Fourier transform and get the frequency components - spectrum of the signal. Which is a very useful concept, when talking about electromagnetic signal for example. In this case, instead of guessing which frequencies are present in your complex signal, by looking to the spectrum you can see it immediately.

You can check for example youtube videos on the spectrum analyzers, in order to see the application for yourself.

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    $\begingroup$ Thank you for the answer, I knew the fourier transform, but what about the intersection of two wave functions in the plot. What would happen when two wave functions intersect in a Fourier series representation of periodic signals? @Pierre Polovodov $\endgroup$
    – Kevin
    Jul 27, 2022 at 9:15
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    $\begingroup$ @Kevin, what do you mean for intersection? Do you mean two wave functions with the same frequency or different frequency, do you consider the same phase? $\endgroup$ Jul 27, 2022 at 9:33
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    $\begingroup$ I am referring to the intersections we can see visually in the plot above. There are four wave functions in the plot and they have the different frequency. But they will intersect when they share the same y values. But that's just the mathematical meaning, and I want to know what the physical meaning of this intersection is? @Pierre Polovodov $\endgroup$
    – Kevin
    Jul 27, 2022 at 10:16
  • $\begingroup$ If I understand your issue correctly, there are four functions describing the objects orbits and there is a blue curve with a frequency $f$, the red one $2f$, the other ones are multiples of $f$. The thing is that, the curves will intersect when the phases are equal, for exemple $2\pi f t + 2 \pi= 2\pi 2 f t$ etc. $\endgroup$ Jul 28, 2022 at 9:17
  • $\begingroup$ yes, it is. I want to confirm if it suggests that their phases are equal when intersect and what would happen when intersect. Will the intersection cause phase shift? $\endgroup$
    – Kevin
    Jul 29, 2022 at 9:44

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