Fourier derivative

A numerical differentiator for periodic functions using Fourier transformations

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.