Fourier Series Approximations

🎵 How Your Phone Stores 1000 Songs

Your voice saying "hello" contains maybe 50 different frequencies mixed together.

MP3 compression: break the sound into frequencies, delete the ones you can't hear (above 20kHz, below 20Hz), keep the rest.

Result: 10% of original size, sounds identical.

The math behind this? Fourier decomposition — the visualization above.