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How to perform FFT from plane-wave basis function coefficients to real space?

The whole point of the FFT is to avoid the costly matrix-vector multiplication of the DFT, which has an effort of $\mathcal O(N^2)$ (where $N = N_x N_y N_z$), and perform the unitary transformation ...
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Computing numeric derivative via FFT - SciPy

Here we have $L=NT=2\pi$ (the total duration for which the signal was sampled), with the fundamental frequency $ω_o=\frac{2\pi}{NT}=\frac{2\pi}{L}=1$, slight modification of the code yields the ...
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