Fourier Series Animation using Circles #fourier

Any periodic signal can be decomposed into a set of simple oscillating functions (also known as harmonics) via the application of Fourier series expansion. Here, we demonstrate a few harmonics using circles and how they add up to obtain the resulting function. Each circle spins at a multiple of a certain fundamental frequency. First, we show each harmonic individually and later show what they add up to and how the circles can be used for their visualization.

Same visualization but for the sawtooh wave:

The code for the animation can be found at

Cite as:

[meyavuz]

Same visualization but for the sawtooth wave:

[oussamaitrbi]

This is well done. So nice to watch this illustration.

[Maxisokol]

So nice. Much beautifull. Very wow. :)

[ioncasu]

THANKS! THANKS! THANKS! THANKS! THANKS! THANKS! THANKS!

[assadij]

I love this...  I can watch it for hours :)

[raghukrao]

Excellent illustration concept and animation. Equation at 0:24 has typo btw. Also, maybe you should show what happens on the projection from above on X axis :-)

[joeyperez]

i teach practical vibration analysis for machinery diagnostics, this is very good visual aid..
thank you much.

I don't understand one thing: in 0:27 you move circles. Why? What does it mean?

[SSLaplaceTransform]

Very nice! Your explanation is "Feynman-esk".

[MechanicalEI]

+meyavuz, beautiful illustration. Although, would have loved if you offered a little more explanation. Thanks for uploading!

[meyavuz]

MMaurice Bendou Yes this is done using Matlab.

[samasd]

Great animation illustrating FFT by phasor addition!   That helps visualize the FFT function much easier than typical explanations-- wish I'd seen it years ago.    Can you illustrate an IFFT with phasors?

[isaacelesemoyo]

Is there a way to make one of the circles rotate in a clockwise direction, preferably the smallest one?

[BrekMartin]

If the radius of the largest circle is 10.0 units, what is the radius of the three smaller circles?

[zaxioms]

How do you get the radii for the circles