Preview · progress not saved — Chapter 1 is free
From MP3s to Instagram filters
Time domain (left) vs frequency domain (right): same sound, two different views
Equalizer: each slider controls one frequency range independently (Fourier components)
JPEG compression: remove high frequencies humans barely notice, keep low frequencies
Square wave built from odd harmonics: 1st, 3rd, 5th, 7th... frequencies
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.
Think in frequencies for audio and images
In the visualization, adding more circles (more terms in the Fourier series) makes the approximation better. Mathematically, the infinite series converges to the exact square wave. In practice, why stop at finite terms?