How to make complex waveforms with sinewaves, the power of Fourier

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Some members on this site seem to deny Fourier because they dont believe you can break up complex musical signals into just sinewaves and all that implies when testing electronics with such. Heres an interesting video showing very complex waveforms made from constant amplitude sinewaves, might change a mind or two.

YouTube

and the math and process

YouTube
 
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Some members on this site seem to deny Fourier because they dont believe
you can break up complex musical signals into just sinewaves

To clarify, a repetitive waveform has a discrete spectrum.
However, a nonrepetitive waveform has a continuous spectrum
which contains all frequencies.

This shows both the sinc envelope of the discrete spectrum of a
repetitive pulse, and also the continuous sinc spectrum of the
corresponding single pulse. Lecture 3
http://www.montana.edu/aolson/eele445/lecture_notes/EELE44514_L3-5.pdf
 

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