Fourier Series
Sum harmonics to approximate periodic signals. Adjust amplitudes of sine/cosine terms and see convergence toward square, sawtooth, or custom shapes.
Who it's for: Signals, acoustics, and advanced math; synthesis vs analysis view.
Key terms
- Fourier series
- harmonics
- superposition
- periodic function
- synthesis
How it works
Finite **Fourier sums** approximating periodic targets: **square** (odd sines), **sawtooth**, and **triangle** (odd sines with 1/k²). Raise the term count to see convergence; near jump discontinuities you still see **Gibbs overshoot** (square/saw). The dashed curve is the ideal limit; cyan is the partial sum. Toggle **animate** to slide phase in time.
Key equations
Frequently asked questions
- Why do sharp corners need many harmonics?
- Discontinuities or sharp bends require high-frequency content to approximate; smooth waves need fewer terms for a good fit.
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