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Use Fourier transforms to calculate derivatives
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[QUICK DESCRIPTION] One can calculate the derivative of a function $f(x)$ by calculating its Fourier transform $\hat{f}(k)$, then calculating the inverse Fourier transform of $ik\hat{f}(k)$ (where $i$ is the square root of minus one). This method is tedious for analytic functions, but is very convenient if one needs to calculate the derivative of a function that is defined as a discrete data set. [PREREQUISITES] Fourier analysis [EXAMPLE] [GENERAL DISCUSSION]
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