Fourier Analysis

Any wave can be built from simple sine waves

Wave Type

Harmonics 5

Speed

Result: Sum of All Harmonics f(t) = Σ sin(n·ωt) / n

Individual Harmonics (Component Waves)

The Big Idea

Joseph Fourier discovered in 1822 that any periodic wave—no matter how complex—can be expressed as a sum of simple sine waves.

"Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them."

— Joseph Fourier

A square wave looks nothing like a sine wave. But add up the right sine waves at the right frequencies, and you can build one perfectly.

Each harmonic is a sine wave at a multiple of the base frequency:

1st harmonic: 1× frequency
2nd harmonic: 2× frequency
3rd harmonic: 3× frequency
...and so on

The amplitude of each harmonic determines how much it contributes. Different patterns of amplitudes create different wave shapes.

🎵 Audio compression (MP3, AAC)

📷 Image compression (JPEG)

📡 Signal processing

🔊 Noise cancellation

🩺 Medical imaging (MRI)

📊 Stock market analysis

🌊 Ocean wave prediction

Any time you need to analyze what frequencies are present in a signal, Fourier analysis is the tool.