Fourier synthesis

This is to show how you can build a periodic signal (a sound that you can hear) with sines (actually cosines):

Expansion:First choose a saturated cosine, a square signal, a rectified cosine or triangle signal (choose curve on top line). Vary the frequency, the amplitude and phase and play it.
Then click on add comp to let the computer generate the first component (cosine) of the fourier expansion.
Click again on add comp for the second non negligible component : a cosine at triple frequency for a square wave. Click again to get next component.
See them on lines 1, 2 ...and check the synthesis (see it on top line, or listen to it).The experiment is better with the saturated signal.
You can adjust frequency amplitude and phase for each component, see the result. A component is selected by clicking on it.

Nota: Sometimes synthesis is not complete with cosines, a DC (average) component has to be added (e.g. rectified signal)

First order low pass filter:Build the default square wave (duty cycle 50% i.e. phase 0°!)and expand it into components. Consider the action depends on the frequency of a filter :

Adjust the 1st component at f=110, vol= 27177 (95% of 28 648), phase=108 (90+18).

Adjust the 2nd component at f=330, vol= 6752 (70% of 9549), phase=108 (90+45).

Adjust the 3rd component at f=550, vol= 2948 (51% of 5730), phase=108 (90+59).

Adjust the 3rd component at f=770, vol= 1612 (95% of 4093), phase=108 (90+67).

And look at the synthesis which is the output of such filter.
Also, for musicians : notice that the harmonics correspond to the notes which sound O.K.(harmonious) with the fundamental note. Harmonic with double frequency is the octave, triple :fifth note upper octave : major third ...
for electronicians : the curves are ordered from top to bottom with the color code of resistors (0: black, 1: brown, 2:red etc.)! Enjoy, and give feedback to me.