## Fourier derivative

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A numerical differentiator for periodic functions using Fourier transformations

Updated 3 Jan 2013

Spectral methods of solving partial differential equations may involve the use of a Fourier transform to compute derivatives. If f is a uniformly sampled periodic function containing an even number of elements, then fourierderivative(f) computes the derivative of f with respect to the element spacing. For best results, f should be periodic such that f(x + a) = f(x + b). As an example,

x = linspace(0,pi);
f = exp(cos(x).*sin(2*x));
dfdx = fourierderivative(f,0,pi);

Results for nonperiodic f are dubious.

### Cite As

Matt (2023). Fourier derivative (https://www.mathworks.com/matlabcentral/fileexchange/39700-fourier-derivative), MATLAB Central File Exchange. Retrieved .

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