Square Waves FFT Analysis
Interactive visualization of square waves at multiple frequencies. Square waves are characterized by their abrupt transitions and contain a rich spectrum of odd harmonics.
About Square Waves
Characteristics
- Sharp transitions: Instant switching between +1 and -1
- Digital-like: Represents binary signals (ON/OFF)
- Rich harmonics: Contains all odd harmonics (3f, 5f, 7f, 9f...)
Frequencies
This demo shows 3 different frequencies:
- 3 Hz - Low frequency (orange)
- 8 Hz - Mid frequency (yellow)
- 20 Hz - Higher frequency (lime)
Harmonic Content
The FFT spectrum of a square wave shows peaks at:
- Fundamental (f): The base frequency
- 3rd harmonic (3f): 1/3 amplitude
- 5th harmonic (5f): 1/5 amplitude
- 7th harmonic (7f): 1/7 amplitude
- And so on...
The amplitude of each harmonic decreases as 1/n where n is the harmonic number.
Why Only Odd Harmonics?
Due to the symmetry of the square wave (half-wave symmetry), all even harmonics (2f, 4f, 6f...) cancel out, leaving only odd harmonics.
Filter Effects
| Filter | Effect on Square Wave | Visual Result |
|---|---|---|
| Low Pass | Removes harmonics, rounds edges | Smoother, more sine-like |
| High Pass | Removes fundamental, keeps edges | Spike-like |
| Band Pass | Isolates specific harmonics | Modified shape |
Mathematical Definition
Square wave using Fourier series:
y(t) = (4/π) × [sin(ωt) + sin(3ωt)/3 + sin(5ωt)/5 + ...]Where ω = 2πf (angular frequency)