Mathematics
Fourier Series for Representing Periodic Functions Beyond Sines and Cosines
Quick fact
The trigonometric Fourier series is just one of infinitely many ways to decompose a periodic function; functions can be represented using any complete orthonormal set, such as complex exponentials, Walsh functions, or Haar wavelets, each highlighting different features of the signal.
Why this is interesting
You've heard that any repeating wave can be built from smooth sine waves—but what if we used square waves or even random-looking blips instead? The music might sound different, but the information would be exactly the same.