First and Second Derivatives of a Periodic Function Using Discrete Fourier Transforms

Consider the family of periodic functions , where . This Demonstration applies the discrete Fourier transform to compute the first and second derivatives of . (The derivative order 0 gives the original function.) The derivatives obtained analytically are shown in dashed red, while the numerical solutions are shown in blue. For a large number of sample points, there is close agreement between the two methods.

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