# How to design an experiment that shows that a rectangular pulse can be expressed as a series of infinite sinusoids?

Is it possible to design a physical experiment that shows that a time limited signal, such as a rectangular pulse is composed of infinite continuous sine/cosine waves?

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this might give you ideas of how to go about it en.wikipedia.org/wiki/Fourier_series . For a single pulse see en.wikipedia.org/wiki/Rectangular_function . One could build electronic circuits which would reproduce the effect on a screen –  anna v Feb 16 at 8:21
I have to say that as described you are talking about a mathematical fact. It not something that is amenable to experimental proof or disproof, it simply is. The experiment asks if the signal does or does not superimpose in linear, non-interfering additive way. You are not testing Fourier decomposition (which is math), but the superposition of your signals (which is a physical property assumed in the mathematics of Fourier decomposition). –  dmckee Feb 16 at 15:26
@dmckee Are you saying mathematical "facts" cannot be showed to be true experimentally? –  user13107 Feb 17 at 8:13
I am saying that mathematics can be true independently of physics. What you test with the mechanisms suggested below is "Do the physics of the signal include the mathematical prerequisites for Fourier composition?" –  dmckee Feb 17 at 16:00

Idea #2: Build an electronic circuit that separates a periodic input signal (e.g. a square wave) into its component frequencies (using an array of band-pass filters) and then adds these signals back together to get an approximation of the original signal.

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Thanks. That seems plausible. I am accepting this now but I hope people will still respond with newer ways f showing this. Most of the attempts so far involve electronics. Perhaps someone can come up with an experiment that doesn't involve building circuits. –  user13107 Feb 17 at 8:17

Idea #1: Build a physical representation of the phasor diagram. Here, each frequency component is represented as a rotating vector, and all of these vectors are stacked end-to-end. In a physical representation, each vector could be a metal bar, and they could be geared to rotate at the correct rates.

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