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The quality of a Fourier approximation of a closed curve \(\gamma:\mathbb S^1\to\mathbb R^2\) depends heavily on its parametrization. Below: a square approximated with 1, 2, and 3 nonzero Fourier modes.
The quality of a Fourier approximation of a closed curve \(\gamma:\mathbb S^1\to\mathbb R^2\) depends heavily on its parametrization. Below: a square approximated with 1, 2, and 3 nonzero Fourier modes.