I have a surface(square image) that I would like to aproximate as a 2d dft. Almost all implementations of $X(k) = \displaystyle\sum_{t=0}^{n-1} x(t) e^{-2 π i t k / n}$ I have seen imply that k - the number of bands and t - the number of samples would be the same and probably should be sampled in a lattice-like manner. To my knowledge the sampling is done only to assess how similar harmonic is to a signal. Why can not it be done similar to sampling a spherical function with Monte Carlo methode where we can use any number of samples to assess how similar a spherical harmonic is to the function. I don't need very big number of sinusoids so does it limit the number of samples I can take?
2026-04-17 17:01:29.1776445289
Sampling a signal in 2D DFT
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