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examples
Frequencies Everywhere
From MP3s to Instagram filters
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Time domain (left) vs frequency domain (right): same sound, two different views
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Equalizer: each slider controls one frequency range independently (Fourier components)
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JPEG compression: remove high frequencies humans barely notice, keep low frequencies
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Square wave built from odd harmonics: 1st, 3rd, 5th, 7th... frequencies
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concept
🎵 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.
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quiz
Apply Fourier Thinking
Think in frequencies for audio and images
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You're building noise-canceling headphones. You sample ambient noise, analyze frequencies, and play inverse waveforms. The math behind 'analyze frequencies' is: