Suppose I have a 2d function defined on a square of length $L$, that is given as an $N \times N$ matrix of values.
The resolution to which we know the function is $\delta L = L/N$. We may take the (discrete) Fourier transform of the image, which will return an $N \times N$ matrix of complex values.
My question is, what is the resolution $\delta k$ of the Fourier transformed matrix in terms of $N$ and $L$?