Fourier, 200 years ago showed you can create a curve of any shape you can imagine by adding Sine Waves. The synth applies that to music and speech.
But the concept is applied in hundreds of fields as you move from curve, to planes to volumes.
The key magic is the sine wave which unlike other curves on differentiation any number of times always produces a sine way due it's deep connection to anything in nature that Repeats.
Sine waves are convenient, but aren't at all necessary for a fourier transformation. The requirements are that you have a set of functions which are all pairwise orthogonal which also form a complete basis set.
At least, that is what I recall from my EE classes 35 years ago.
But the concept is applied in hundreds of fields as you move from curve, to planes to volumes.
The key magic is the sine wave which unlike other curves on differentiation any number of times always produces a sine way due it's deep connection to anything in nature that Repeats.