🌊
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
- 1Set the frequency, amplitude, and phase of sinusoidal components
- 2See the Fourier series synthesis in real time
- 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
🔗 Related Tools
🧭
ベクトル計算機ベクトル計算【無料・ビジュアル】2D/3Dベクトルの和・差・内積・外積・射影をドラッグ操作でインタラクティブに可視化。大学の線形代数・物理の学習に。
📐Sequence CalculatorCalculate terms and sums of arithmetic, geometric, and Fibonacci sequences.
📐微分積分ビジュアライザー微分積分【無料・ビジュアル学習】関数の接線・積分面積をリアルタイム描画。微分・積分の概念をアニメーションで直感的に理解。リーマン和・シンプソン法対応。
📈Graph PlotterPlot math functions in real-time with multiple curves, zoom and pan.
All calculations run in your browser. No data is sent to any server.