CCalcBOX
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フーリエ級数ビジュアライザー

フーリエ級数【ビジュアル学習】回転ファゾールが波形を合成するアニメーションで直感的に理解。方形波・三角波・ノコギリ波・ギブス現象を体感。信号処理の学習に。

Fourier Series Visualizer

Watch rotating phasor vectors add up in real-time to synthesize a waveform

Phasor Animation
Waveform Synthesis
5 terms
1.0x
Gibbs Phenomenon⚡

Overshoot near discontinuity: 8.9%

Color Legend

n=1
n=3
n=5
n=7
n=9

∑Series Formula

f(x) = 1.273·sin(1x) + 0.424·sin(3x) + 0.255·sin(5x) + 0.182·sin(7x) + 0.141·sin(9x)
Square wave: bₙ = 4/(nπ) [odd n only] | Theoretical Gibbs overshoot ≈ 8.9%
📖How to Use
  1. 1Set the frequency, amplitude, and phase of sinusoidal components
  2. 2See the Fourier series synthesis in real time
  3. 3Watch how adding more harmonics brings the waveform closer to the original
💡Tips & Knowledge
  • •Fourier transform decomposes complex waveforms into sums of simple sinusoids — the foundation of audio and image processing
  • •A square wave can be approximated by summing odd-numbered harmonics — visualizing this builds deep intuition
  • •MP3 compression applies Fourier transforms to audio and removes frequency components inaudible to humans

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