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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.


Fourier analysis

Example 1

General discussion