Dirichlet Kernel & Gibbs Phenomenon Explorer
Dirichlet Kernel Formula
\[ D_n(x) = \sum_{k=-n}^{n} e^{ikx} = \frac{\sin\left((n+\frac{1}{2})x\right)}{\sin(x/2)} \]
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Visualization
About Gibbs Phenomenon
The Gibbs phenomenon describes the oscillatory behavior near discontinuities in Fourier series approximations. Despite increasing the number of terms, the overshoot remains about 9% of the jump discontinuity.
This tool visualizes how the Dirichlet Kernel \( D_n(x) \) relates to these oscillations in partial sums of Fourier series.